Question

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

24. 64, 144

Short answer

The numbers are not relatively prime andthe greatest common factor is 3

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 64 and 144.

The factors of 64 are: $64=2\times 2\times 2\times 2\times 2\times 2$

The factors of 144 are: $144=2\times 2\times 2\times 2\times 3\times 3$

Step-3 – State the conclusion

From the factorization it can be observed that $2\times 2\times 2\times 2$ is common in both the numbers, therefore, the greatest common factor is 16.