Question

The GCF of two numbers is 871. Both numbers are even and neither is divisible by the other. What is the smallest that these two numbers could be?

Answer 1

The smallest possible numbers are 26 and 134.

Step-by-step explanation:

To find the smallest possible numbers, we need to consider the prime factorization of the given GCF.

The prime factorization of 871 is 13 x 67. Since both numbers are even, they must have 2 as a factor.

Therefore, one number could be 2 x 13 = 26 and the other number could be 2 x 67 = 134.

Answer 2

-- If the GCF of both numbers is 871, then they're both multiples of 871.

-- If they're both even, then they must both be even multiples of 871.

-- They can't be the 2nd and 4th multiples of 871, because then the
bigger one would be divisible by the smaller one.

-- So the smallest they could be is the 4th and 6th multiples of 871 ...

3,484 and 5,226 .

Weird problem !