Finding the GCF

The greatest common factor (GCF) of two numbers can be determined by finding the prime factorization of the numbers. The GCF is the product of the common prime factors. Consider the following pair of numbers. 42,24 The GCF(42,24) will be found by following these four steps.

Find the Prime Factorization of the First Number

Use a factor tree to determine the prime factorization of the first number.

Find the Prime Factorization of the Second Number

Now, follow the same process to find the prime factorization of the second number.

Identify the Common Prime Factors

Write the two prime factorizations together and circle the common prime factors. In this example, the prime factorizations of 42 and 24 will be written together. 42=& 2* 3 * 7 24=& 2* 2 * 2 * 3

Multiply the Prime Common Factors

The greatest common factor of the numbers is the product of the common prime factors of the prime factorization. In this case, the common prime factors of 42 and 24 are 2 and 3. 2* 3= 6 Therefore, the greatest common factor of 42 and 24 is 6.

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