Chapter 4, Problem 8CT

To determine

To find the greatest common factor of 42 & 108

Answer to Problem 8CT

Greatest Common Factor is 6. Hence not relatively prime.

Explanation of Solution

Given information:

Numbers 42 & 108

Formula Used: Factorization

Calculation:

Here, break both the numbers into its factors respectively.

So, 42 may be written as $42=7\times 2\times 3$

And 108 may be written as $108=3\times 3\times 2\times 2\times 3$

As can be seen that $2\times 3$ is common in both the numbers. Hence , the greatest common factor is 6.

When the greatest common factor of two numbers is 1- they are said to be relatively prime.

Since their GCF is not 1, 32 & 90 are not relatively prime numbers.

Conclusion-

Greatest Common Factor is 6. Hence not relatively prime.