Question

In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime if the only positive integer that divides both of them is _____. That is, the only common positive factor of the two numbers is _____. This is equivalent to their greatest common divisor being _____. What number fills in the blanks?

Answer 1

ANSWER

The number that fills in the blanks is 1

EXPLANATION

Two numbers are relatively prime if they have no common factor greater than 1.

For exam 12 and 17 have no common factor greater than 1.

This is equivalent to saying that the greatest common divisor (GCD) of the two numbers is 1.

$gcd(12,17)=1$

This means that $12$ and $17$ are relatively prime.

But

$gcd(12,16)=4$. This means 12 and 16 are not relatively prime or coprime