## Greatest Common Factor of 108 and 42

GCF(108, 42) = 6, Greatest common factor of 108 and 42 is 6. Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the numbers can be divided. There are two different methods to calculate Greatest Common Factor of 108 and 42. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.

### Greatest Common Factor of 108 and 42 by prime factorization method

We will first find the prime factorization of 108 and 42.
Prime Factorization of 108 is 1, 2, 2, 3, 3, 3 and Prime Factorization of 42 is 1, 2, 3, 7.

• Factorize$$(108) =$$ $$1\times 2\times 2\times 3\times 3\times 3$$
• Factorize$$(42) =$$ $$1\times 2\times 3\times 7$$
Now we need to find any which are common for each number (1, 2, 3) and multiply these numbers together.
$$GCF(108, 42) = 1\times 2\times 3 = 6$$.

### Greatest Common Factor of 108 and 42 by matching factors method

List of positive integers factors of 108 leaving a remainder zero is 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
List of positive integers factors of 42 leaving a remainder zero is 1, 2, 3, 6, 7, 14, 21, 42
As you can see, 6 is the greatest and common number that 108 and 42 divides into.
So the greatest common factor 108 and 42 is 6.
$$GCF(108, 42) = 6$$.

Greatest common factor of:
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