# Relatively Prime Numbers and Polynomials

Two numbers are said to be relatively prime if their greatest common factor ( GCF ) is .

Example 1:

The factors of are .

The factors of are .

The only common factor is . So, the GCF is .

Therefore, are relatively prime.

Example 2:

The factors of are .

The factors of are .

The greatest common factor here is .

Therefore, are not relatively prime.

The definition can be extended to polynomials . In this case, there should be no common variable or polynomial factors, and the scalar coefficients should have a GCF of .

Example 3:

The polynomial can be factored as

.

The polynomial can be factored as

.

are relatively prime, and none of the binomial factors are shared. So, the two polynomials

are relatively prime.

Example 4:

The polynomial can be factored as

.

The polynomial can be factored as

.

The two polynomials share a binomial factor:
.

So

are not relatively prime.