Expressions

What is the difference between the greatest and the smallest numbers which are divisible by 8 and are formed by using the digits 2, 4 and 6 each only once?


The answer is 360.

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12 solutions

Pulkit Gopalani
Dec 13, 2013

We know that, Greatest number divisible by 8 formed using 2,4,6 only once is 624.(8x78). Such that smallest no. is 264(8x33). Difference=624-264 => 360 (ans.)

Kingsley Bunni
Dec 14, 2013

well. for a number to be divisible by 8........ the last TWO digits of the number should be divisible by 8 ! and the number is a 3 digit no. given the conditions! so the last TWO digits can be either 24 or 64. so smallest no. is 264 & greatest no. is 624. difference= 624-264=360

Are you sure that is the rule of divisibility of 8? Does it only depend on the last 2 digits? Is 108 a multiple of 8?

Calvin Lin Staff - 7 years, 5 months ago

last two digit is for 4 if last 3 digits are divisible by 8 then only the number is divisible by 8

Chaitanya Lodha - 7 years, 3 months ago
Andy Zhang
Dec 14, 2013

Using the digits 2,4,6 once, the biggest number we get is 642. But 642 is not divisible by 8, so we go on to 624 which is divisible by 8. In the same way, we get the smallest is 264 Thus, the difference between them is 360

Muddasir Lone
Dec 14, 2013

624 is the greatest number by using 2,6 and 4 digit only onces and divided by 8 264 is the smallest number by using 2,6 and 4 digit only onces and divided by 8 therefore the difference between greater number and smallest number is 624-264=360

We all know that there can be 6 possible numbers, so just use the divisibility 8 rule to know the smallest and the biggest, then subtract smallest to biggest.

Mansi Kela
Mar 7, 2014

the greatest no will be 624 and the smallest no will be 264 the difference of these no are 360

Mohammad Fiyaz
Jan 28, 2014

greatest number that is formed from 2,4 and 6 digit each only once and divisible by 8 =624

smallest number that is formed from 2,4 and 6 digit each only once and divisible by 8 =264

thus difference between the greatest and smallest number which are divisible by 8

=>624-264=360 that is answer.

Tushar Parashar
Jan 21, 2014

for it to be divisible by 8 the last 3 digits should be divisible by 8 here greatest no. formed = 624 smallest no. formed = 264 the difference = 624-264 = 360

Kunal Dethe
Dec 14, 2013

The Greatest no. formed by 2,4,6 divisible by 8 is 624 .

The Smallest no. formed by 2,4,6 divisible by 8 is 264 so Their Difference will be 360 .

please why 624-264

Mohamed Hesham - 7 years, 6 months ago
Tariq Anwar
Dec 14, 2013

check for numbers...we first find 264 which is smallest that i divisible by 8 and then 624 which is greatest.....calculate the difference 624-264=360

Justin Stevens
Dec 14, 2013

For the largest number, we look for a number beginning with 6 6 . As a quick check 600 0 ( m o d 8 ) 600\equiv 0\pmod{8} therefore we need the last two digits to be divisible by 8. Among 24 and 42, only 24 is divisible by 8 therefore the largest such number is 624. The smallest will likely begin with 2. We notice that 200 0 ( m o d 8 ) 200\equiv 0\pmod{8} therefore we need the last two digits to be divisible by 8. Notice that 64 is and 46 isn't, therefore the smallest is 264 264 . The answer is henceforth 624 264 = 360 624-264=\boxed{360}

Parth Kohli
Dec 13, 2013

An easy way to solve this is by using simple brute force, since there are only 6 numbers that can be formed using this three digits. The highest number formed by these numbers is 642 642 , which is not divisible by 8 8 . The next is 624 624 , which visibly is. Similarly, the smallest such number should be 264 264 . Hence, the answer is 624 264 = 360 624 - 264 = 360 .

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