Do You Know The Trick For Finding The Units Digit?

What is the units digit of

123 × 456789 ? 123 \times 456789 ?


The answer is 7.

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78 solutions

Muhammad Shariq
Jan 2, 2014

123 3 ( m o d 10 ) , \large 123 \equiv 3 \pmod{10},

456789 9 ( m o d 10 ) , \large 456789 \equiv 9 \pmod{10},

123 × 456789 27 7 ( m o d 10 ) \large \therefore 123 \times 456789 \equiv 27 \equiv \boxed{7} \pmod{10} .

I grasp your solution but it's quite confusing for those who are not mathematician just make it simple for universal understanding...for universal concern they already know the unit word...why not multiply the last digit of two factor 3 and 9 and their product is 27, unit digit is 7 and there every level of knowledge could get it.

Oiledor Origos - 7 years, 5 months ago

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well since you did the explanation for me, I don't need to say anything more ;]

Muhammad Shariq - 7 years, 4 months ago

Wow nice explanation Oliedor, now I actually understand it. I struggle with math alot, so I use brilliant to help myself. Thanks. :)

mark chernioglo - 5 years, 8 months ago

Since the units digit is not affected with any carry from previous multiplications...simple the number in units digit of the product of the last two digits of the given number will be the answer

Vijay Mutyala - 7 years, 4 months ago

plz make 120 using 5 zeroes

Abhijith Krishna - 7 years, 5 months ago

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0 Factorial=1 (0!+0!+0!+0!+0!)!, (1+1+1+1+1)!=5!=120; lets enjoy

venkappa Bhajantri - 7 years, 5 months ago

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multiply the numbers of the telephone how much do u get?

swetha vaidyanathan - 7 years, 4 months ago

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@Swetha Vaidyanathan answer is 362880

archana raghavan - 7 years, 4 months ago

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@Archana Raghavan archana sister how to did it multiply the numbers of the telephone how much do u get?

venkappa Bhajantri - 7 years, 3 months ago

123X456789=56185047 Last digit is 7

Sajjad Hossain - 7 years, 4 months ago

Just multiply 3 by 9, the answer is 27. So, the last unit will probably be 7.

Nichapat Panutyotin - 7 years, 4 months ago

What's the theorem behind this and where can I find it proved or explained?

Ben Haffner - 7 years, 5 months ago

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Basically the idea behind the units digit is that a number in base 10, when divided by 10, whatever remainder that it leaves behind will be the units digit. Hence we take the number modulo 10 to see wat the remainders are. Taking 123 modulo 10 we know the remainder is 3 when 123 is divided by 10, i.e. the units digit is 3. Similarly when 456789 is divided by 10, the remainder is 9, hence 456789 is congruent to 9 modulo 10. Multiplying these two congruences we find that the product as a remainder 27 when divided by 10, but since 10 can go in to 27 two more times, we will have that the remainder will be 7, which implies that the units digit of the product will be 7.

Muhammad Shariq - 7 years, 5 months ago

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Thank you for explaining! I understood the basic concept, but I really wanted to know what the reasoning behind the idea that we can multiply the two congruencies. I've been having problems with the techniques trainer, so I can't look it up there...

Ben Haffner - 7 years, 5 months ago

You are very much clear. But simple is multiplying 3 and 9.

Mohammad Chhiddikur Rahman - 7 years, 5 months ago

In fact, this is the real answer in mathematic form, since it can determnie not only the unit, also maybe the 2 last digit or whatever.

Alvian Hilman - 7 years, 5 months ago

simply multiply these 2 num then the unit (last num) in the becoming answer is is unit num and that is 7

Ghulam Muhiudin - 7 years, 5 months ago

7 ans kesa aya help me

fareeha baloch - 7 years, 4 months ago

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by multiplying the last digits of both the numbers i.e 123 x 456789.

Hanzala Khan - 7 years, 4 months ago

superb question

king Choudhary - 7 years, 4 months ago

I have followed the same method

Mohammad Chhiddikur Rahman - 7 years, 4 months ago

Since the units digit is not affected with any carry from previous multiplications...

Vignesh Madurai - 7 years, 4 months ago

7

Amit Mishra - 7 years, 4 months ago

who will answer:::::::------

The lengths of two cubes are positive integers. The difference between their volumes can be found from the set {8, 7, 11, 21, 23, 15, 29, 33, 37, 39}. Find all possible lengths of the smaller cube.???

Sälmän Rähmän - 7 years, 4 months ago

to find out the units digit of 123 x 456789 is just by multiplying 3 with 9 and then by paying attention to the units digits of 3x9....finally we got 7

rusli azis - 7 years, 3 months ago

good enough...thnx

Arvind Krishna - 7 years, 3 months ago

What is the units digit of 123X456789=56185047 Last digit is 7

bharati kumbar - 7 years, 3 months ago

what is (mod 10)

jalal uddin - 7 years, 5 months ago

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[mod or %] is an binary operator such that a % b will give the remainder value when a is divided by b..

Varun Chaturvedi - 7 years, 4 months ago

yr mjhe to smjh nh arha kch smjhao kch :/

fareeha baloch - 7 years, 4 months ago

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In what language is this again?

Lanvin De Los Santos - 7 years, 4 months ago

fareeha kia smj nahi aya ??? unit digit ho hota ha jo unit place pe ho kisi bhi quantity ma ....

Nadia Khan - 7 years, 4 months ago

thats the most easy answer yaar.....multiply the first unit's place in both the nos. i.e 3 X9=27 where 7 will be the unit place whatsoever the other number be....simple

Minthang Lhouvum - 7 years, 4 months ago
Hùng Minh
Jan 3, 2014

The units digit of 123 × 456789 is equal the units digit of 3 * 9 <=> the result is 7

Yeah,I got it

Saifunnahar Tonby - 7 years, 5 months ago

not understand~please explain

Fauzi Bakri - 7 years, 4 months ago

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"What's the problem with you?" Tell me what you don't understand?

Hùng Minh - 7 years, 4 months ago
Blazer Raza
Jan 3, 2014

If we want to find the unit of any long or short number multiplied by any number, we could find it by multiplying the last digit with last digit, then from the answer the unit of the answer will be the correct answer. Eg: 3*9=27 so the unit of it will be the unit of total. Answer is 7.

Ramya Rams
Jan 16, 2014

multiply only unit digit place values 9*3=27 and unit'splace value ans will be 7

right. It is the easyest way.

Mohammad Chhiddikur Rahman - 7 years, 4 months ago

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yes

Ramya Rams - 7 years, 4 months ago
Ghulam Muhiudin
Jan 12, 2014

First of all you multiply 123*456789 then the becoming ans will be 56185047 ... then u know hat the extreme last number is a unit ... THEN the unit in this answer is (7).

Aashi Jain
Jan 3, 2014

123*456789=56185047 so unit digit is 7

But more easy is to only multiply 3 and 9.

Reeshabh Ranjan - 7 years, 5 months ago

:P

Ameer Hamza - 7 years, 5 months ago

Yup 9*3 why waste unecessary time to find out the unasked..:P

Soumya De - 7 years, 5 months ago

I have followed it

Mohammad Chhiddikur Rahman - 7 years, 5 months ago

what is unit digits??

Fauzi Bakri - 7 years, 4 months ago

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Thank you to fell free to question. The units digit is the rightmost digit of the number. For example for the number 327, 7 is the units digit and means 7 units i.e. 7 ones, giving a total of 7 2 is the tens digit and means 2 tens, giving a total of 20 3 is the hundreds digit and means 3 hundreds, giving a total of 300

Mohammad Chhiddikur Rahman - 7 years, 4 months ago
Jaimeline Marcelo
Jan 11, 2014

123*456789= 56185047 so as you can see 7 is in the units so 7 is the answer

Ria Patel
Jan 4, 2014

There is no need to do the whole multiplication problem. Just multiply the units digit of 456789 by the units digit 123. 9x3= 27, and the units digit of 27 is 7. Therefore 7 is the answer.

you need not multiply the complete number.instead multiply the last digits 3 x 9 = 2(7) so 7 is the correct answer

Diana Taha
Jan 3, 2014

the units digit is the rightmost digit of the number. For example for the number 327, 7 is the units digit and means 7 units i.e. 7 ones, giving a total of 7 2 is the tens digit and means 2 tens, giving a total of 20 3 is the hundreds digit and means 3 hundreds, giving a total of 300

so if the rightmost (i.e. units) digit of a number is even, then the number is divisible by 2

Siddharth Sid
Oct 15, 2014

3*9=27... only 7 remains the units digit

Yusra Memon
Apr 30, 2014

Multiply the unit digits of both number which are 3 and 9 , we got 27 in which 7 is unit digit.. So answer is 7

Tirthankar Ghosh
Mar 31, 2014

Multiply 3 and 9 , the last digits of the two numbers and you'll get 27 whose unit digit is 7

Julieta Ramos
Mar 29, 2014

The last digit of any number is called unit.When we multiply 123 x 456789 = 56185047, so the last digit 7.

Abhinav Ankur
Mar 21, 2014

The answer is 7

Datu Oen
Mar 12, 2014

When you multiply two numbers, the last digit of the product is the last digit of the product of the two numbers. So the last digit of 123 x 456789 comes from the last digit of the product of 3 and 9 which is 7.

Just take the unit digit of each number ,multiply the one-digit numbers and take the last digit of the product of the multiplication.In this case 12 3 45678 9 . 3 9 = 2 7 12\boxed{3}*45678\boxed{9}. 3*9=2\boxed{7}

3 * 9 = 27 hence 7 is the units digit.

Ken Ken
Mar 6, 2014

multiply 123 by 456789 then the result will be 56185047. unit digit is also known as ones digit. in the result, 7 is the ones digit.

Adrian Delgado
Mar 2, 2014

By multiplying the last digit (3 and 9) get 27. So, the number of units of the product is 27.

Kajal Jain
Feb 27, 2014

123x456789=56185047 and the unit place is 7

Sai Kiran
Feb 15, 2014

units digit is nothing but the last digit so on multiplying the last digits of the two numbers i.e., 3 & 9 by multiplying these 2 numbers we get 27 and the last digit of this number is 7

Debolena Basak
Feb 15, 2014

multiply the units digit of both the no.s..its 27..unit digit in 27 is 7.so the ans is 7

Alok Rathaur
Feb 12, 2014

3*9=27 unit place is 7

7

Debajyoti Bhowmik
Jan 30, 2014

unit digit of multiple*unit digit of multiplier=7

Sai Subbu
Jan 29, 2014

we can just multyply unit digits ie 3 * 9=27 and the unit digit of 27 is 7 will be the unit digit of the 123*456789

Waqar Sajjad
Jan 27, 2014

just multiply unit digits of both values

It's simply as same as the units digit of 9x3 = 27.. so, the units digit is 7..

Raja Prabu
Jan 23, 2014

Multiply the last digit(Unit digit) of two numbers(123 & 456789) and take the unit digit from the result Step1: last digit of 123 is 3 and last digit of 456789 is 9 Step2: 3*9=27 Step3: Unit digit(last digit) of 27 is 7 Answer is 7

Devwritt Arya
Jan 23, 2014

3*9=27 and 7 is unit digit.

Siddharth Jain
Jan 23, 2014

All you need to do is, multiply both units digit to get the answer. i.e. 3*9 =27. Now, 7 will be the units digit while 2 will be carried over!

Shayantan Mondal
Jan 23, 2014

simply mulitiply the 2 no. and done its only 2nd unit and see the result

Archit Murkunde
Jan 22, 2014

123 x 456789=56,185,047......7 is in the units place

Bhushan Reddy
Jan 22, 2014

3X9=27 so last digit is 7

Mohammad Fiyaz
Jan 22, 2014

123x456789=? there is no need to multiply all the digits. as we know that we have to find only units digits, by multiplying only units digits we can find unit digit of above problem. It's quite easy.

Sultan Firdaus
Jan 22, 2014

it's simple 2 + 5 = 7

Putta Sadhana
Jan 22, 2014

multiply the last digits and write the units digit of the product. 123 456789. multiply 3 and 9. 9 3=27. 7 is the units digit of the product .so 7 is the units digit of 123*456789

A digit in a number has two weights, one face value and the other power value. The power value in a number system is a power of the base. In decimal category the power value is a power of 10 beginning from the least whole number. The unit place has the power value 1 . In order to find the number in the unit place of the product you have to multiply the corresponding elements in the numbers to be multiplied and get the unit digit value.. So in our example we get 27(3x9) and the unit place in 27 is 7.. too simple but confusing for a beginner. .

basic multiplication......multiply the units digit of the 2 given numbers and take the units digit of the product that is your answer

Shashank Raj
Jan 21, 2014

the easiest way to multiply any number is......for example.. (45x24).... just multiply the first two digits to the the first digit of the answer that is the first digit of 45x24 is 8 and now multiply the across numbers and add them up..... that is 4x4 +5x2=26 .... so now if the answer u get is of a single digit than directly write the number besides the first digit of the answer ....if it is a double digit number tha add the first digit of it to first digit of the answer and next to write the number which is left and than at last multiply the last two digits of the number and proceed as the above ..(that is 5x4=20) than add it to the answer tha this is how u get it ..... the solution of (45x24=1080)...... that is add the first digit of 26 to 8 which is 10 and write the letter besides 10 which is nothing but 6 in the given problem that is 106 now add the first digit of 20 to the number 6 which is 6+2=8 and write the remaining number besides it which is 0 which equals to 80 now combine the complete number that is 1080 .... which is the answer of (45x24)..... friends the procedure which i hav texted is very long but dont think that the method is very long ......actually it is very short and easy ..and we get accurate answers with it and u can multiply any number with any other number by this method very easily

Pearl Loterte
Jan 20, 2014

The unit digits of the two factors are 3 and 9 thus give an answer of 27 and 7 is the unit digit.

Mohamed Rameez
Jan 19, 2014

For finding the units digit,the number in the units digit of the numbers to be multiplied will only make a difference..Therefore 9 x 3 =27 and hence unit digit is 7.

Swapna Mandal
Jan 19, 2014

simply multiply the unit's digits of the two given numbrs.

just multiply unit digit of both the numbers ie. 3*9=27 here the unit digit is 7 hence correct ans. is 7

Parthi Munusamy
Jan 19, 2014

Multiply 3 x 9 and remove all the digits except for the ones digit. The ones digit is your answer.

Suneet Kandulna
Jan 18, 2014

just multiply it and the rightmost digit is the units digit

Rudra Garikipati
Jan 18, 2014

multilply unit digits of both numbers

Sathi Nagi Reddy
Jan 18, 2014

the unit digit of a multiplication is just unit digit of multiplication of unit digit of multiplying numbers. So unit digit in multiplication of 3 and 9 is 7.

Rajput Naresh
Jan 18, 2014

Multiply unit digit of both numbers and in the answer neglect tens digit.

Varun Suvarna
Jan 18, 2014

It is very simple! The units digit of this statement is going to be the last digit of the products of 3 and 9.

Archana Mohanty
Jan 18, 2014

just multiply the units digit i.e.,3 and 9

Simply take the product of the ones digits.

3 9 = 27 3*9 = 27

Since their product is a two-digit number, simply take the ones digit.

The answer is 7 \boxed{7} .

Niraj Singh
Jan 16, 2014

3*7=27 then last digit is 7 and bingo that's the answer!

Akshay Rathore
Jan 15, 2014

just multiply the units digit from both numbers and take the units digit of the result

Renjith R
Jan 15, 2014

the last two numbers are 3 and 9 therefore 3*9 = 27 so unit digit is 7

Shivish Dubey
Jan 14, 2014

product of unit places of both numbers 3*9 =27 ,hence 7 is the unit digit.

Just take the last digit of both numbers and multiply them.From the resulting product take the last digit which is the answer.In the above problem take 3,9 and multiply them 3x9=27.the last digit 7 is the answer

Shireesha Muskam
Jan 13, 2014

take lst digit of bith no. i,e. 3 and 9 then multiply them 3*9=27 then take last digit 7

You are correct

Mohammad Chhiddikur Rahman - 7 years, 5 months ago

9*3=27 so, 7 comes in the units digit

Irfan Wahyudin
Jan 11, 2014

123 x 456789 has 3 as units digit of 123 and 9 as unit digit of 456789 ,..if they are calculated they will have unit digit = 3 x 9 = 27 ,..which the units digit is 7

Nitesh Varshney
Jan 9, 2014

3*9=27 so last digit will be 7

multiply the unit digits of two no's ,the unit place of resultant one is the unit place of whole multiple.

Arul Deepak R K
Jan 9, 2014

To find the unit digit of any multiplication take the unit digits of the numbers. In this case 123 x 456789, Take 3 and 9, multiplication of 3 and 9 is 27 and the unit digit will be 7

Sandeep Naidu
Jan 8, 2014

We can know units digit when we multiply unit digits of the given numbers. So 9x3 = 27 In 27, 7 is the unit digit. Hence answer is 7. Note: Do not follow same method in finding ten's or hundred's etc.. digit of a number

Krati Gupta
Jan 7, 2014

The unit digit of the product of multiplicands is the unit digit of the product of the unit digits of the multiplicands. Therefore, the unit digit of (9 x 3) i.e. 27 is 7. So, the unit digit of (123 x 456789) is 7.

Piyush Chauhan
Jan 6, 2014

Multiply unit digits of both numbers and retain the unit digit of resultant.

Anusha Singadi
Jan 6, 2014

3*9=27 THEREFORE UNTIS DIGIT WILL BE 7

multiplication of unit places will give you 27. so that last digit will come as 7

Brian Traub
Jan 5, 2014

The units digit of any product will be the units digit of the units digit of the first number times the units digit of the second number. In other words, you multiply the numbers in the one's place of both numbers and the number in the one's place of the result is what you're looking for.

Reeshabh Ranjan
Jan 5, 2014

As we know, to know the units digit of a multiplication, we need to only multiply the last digits of the given numbers. So 3*9 = 27, and thus the Units digit comes out to be 7

Dhanya Nambiar
Jan 5, 2014

Only the last digit of the product of the units place of both the numbers , others are 0. 3*9=27 , take 7 which is your answer.

Shafeeq Ahmed
Jan 4, 2014

3 * 9 = 27, units place is 7 so the ans is 7

when u multiply the unit digit of both the numbers that is 3 and 9 you get 27 and 7 is the unit digit of 27 and hence is the answer ...............

Parth Shah
Jan 4, 2014

Since We need to find unit digit of solution, we just have to consider the unit digit of 3*9 and it is 7.

Vasu Bansal
Jan 4, 2014

Just multiply the last two digits of the number. The last digit of the product is the answer

Prasun Biswas
Jan 4, 2014

When any 2 nos. are multiplied, to find the units digit of the product, we can simply multiply the units digit of the two nos. which are multiplied in the question. The units digit of the product of that will be the units digit of the actual product in the question. Here, the given nos. are 123 123 and 456789 456789 which have units digit 3 3 and 9 9 respectively.

So, product of the units digit = 3 × 9 = 27 =3\times 9 = \boxed{27}

The units digit of 27 is 7, so we get the units digit of the product in the question as 7 \boxed{7} .

the units digit is the rightmost digit of the number.so 3 and 9 are two unit digit n since 3*9=27 n 7 is the units digit of 27 so answer is 7

Anjali Kulkarni - 7 years, 5 months ago

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Yes, that's the trick to find units digit for any product of 2 nos.

Prasun Biswas - 7 years, 5 months ago
Sunil Pradhan
Jan 3, 2014

consider only unit digit 3 × 9 = 27 the unit digit of 27 is 7

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