Can the greatest common factor of 16 and 42 be greater than 16?

Answer 1

Well, think about what it means for something (say a number c) to be the greatest common factor of 2 numbers (say a and b *non-zero*).

It means that c is the largest integer such that a and b are both divisible by c.

If c > a, then how can a be divisible by c?

If c > b, then how can b be divisible by c?

Therefore c < a & b

As for 16 and 42:

16 = 2 x 2 x 2 x 2

42 = 2 x 3 x 7

The only shared (or common) prime factor is 2. Therefore the GCF is 2.

Other answer:

No, GCF(16,42) can't be greater than 16.

GCF of two numbers a and b(where a>b) is always smaller than or equal to a.

But why it can't be greater than a?

GCF means greatest common factor, the greatest factor of a is a, and there can be many common factors of a and b. But a(factor of a) is the largest among all the common factors, so GCF can't be greater than a.

Prime factorization of 16 = 2x2x2x2

Prime factorization of 42 = 2x3x7

What is common in the factorization of 16 and 42? Only 2 is common so GCF is 2.