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What is the greatest common divisor of 2 × 3 × 5 2 \times 3 \times 5 and 2 × 5 × 7 2 \times 5 \times 7 ?

1 2 5 7 10 15

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16 solutions

Daniel Chiu
Oct 6, 2013

The greatest common divisor is equal to the product of the lowest power of each prime. In this case, that is 2 1 3 0 5 1 7 0 = 10 2^1\cdot 3^0\cdot 5^1\cdot 7^0=\boxed{10} .

i can't get it...can you please define it any easy way.

Shivanshu Siyanwal - 7 years, 8 months ago
Zack Chatters
Oct 11, 2013

Firstly, you need to know the definition of GCD it means greatest common divisor. Secondly, you must take the numbers they share in this case it is 2 and 5 then multiply them. Finally, the answer appears. 10!

Yaminee Gokhale
Oct 9, 2013

as multliplication of 2x3x5 n 2x5x7 is 30 n 70 respetively so their is 10

Nurin Zunah
Oct 12, 2013

2 x 3 x 5 = 30

2 x 5 x 7 = 70

Both can be divided by 10

Ralph Schraven
Oct 9, 2013

To find out the GCD between two numbers, we first need to write them as prime factors. Now we see that this has been done for us: 2, 3, 5 and 7 are all prime numbers. The GCD of two positive integers is simply the product of all the prime factors they have in common. 2 is in both the numbers, 5 as well. Thus, the answer is the product of 2 and 5, which is 2 × 5 = 10 2 \times 5 = \fbox{10}

Joseph Chan
Oct 8, 2013

The two numbers are split into their individual prime factors. It is therefore easy to find out their greatest common divisor. Since both of them have 2 and 5 as factors, and \frac {7}{3} =/= an integer, therefore the greatest common divisor is 2 \times 5=10.

Azwan Azali
Oct 7, 2013

Compare 2^1 x 3^1 x 5^1 x 7^0 and 2^1 x 3^0 x 5^1 x 7^1 . Take the smallest num of degree and take their product. In this case: 2^1 x 3^0 x 5^1 x 7^0 = 10

Ilham Adiyaksa
Oct 7, 2013

the most number is 2 and 5. So, you just 2x5 = 10

THERE IS COMMON 2& 5 SO 2.5= 10

Aashish Patel
Apr 14, 2014

The greatest common divisor is always the product of the common numbers that appear in both of the prime factorisation.

Anzar Aznzar
Mar 30, 2014

2 * 3 * 5 , 2 * 5 * 7

They both have 2 and 5

x = 2 * 5 = 10

Habeeb Rahman
Oct 13, 2013

10

Tabby Weir
Oct 13, 2013

You multiply the three numbers together for each equation. eg. 2x3x5= 30 2x5x7=70 Common factors of each equation: 2, 5, 10 HCF: 10 Highest common divisor = 10

2 3 5 and 2 5 7,there is 2*5 is common which is 10 and also it is the greatest divisor..thus, 10 is the GCD of these priducts

Appy Padghan
Oct 13, 2013

3 and 7 are non-common factors ....so gcd is 5*2 that is 10

Santosa Wongso
Oct 9, 2013

just look at the same nubers => 2 & 5 so 2x5= 10

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