Question

Find the greatest common factor of the numbers. Then tell whether the numbers are relatively prime.

9, 26

Short answer

The numbers are relatively prime.

Step-by-step solution

Step-1 – Define greatest common factor

A common factor is a whole number that is a factor of two or more nonzero whole numbers. The greatest of the common factors is the greatest common factor (GCF).

Two or more numbers are relatively prime if their greatest common factor is 1.

Step-2 – Factor the numbers

Factor both the numbers 9 and 26.

The factors of 9 are: $9=3\times 3$

The factors of 26 are: $26=2\times 13$

Step-3 – State the conclusion

There are no common prime factors. However, two numbers always have 1 as a common factor. So, the GCF is 1, and the numbers are relatively prime.