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Prime Factorization

How can prime factorization help identify the GCF?

Goal:

Goal:

Another strategy that you can use for finding the GCF of a set of numbers is the use of prime factorization. Prime factorization is a strategy that requires you to factor out each number to only prime factors.

Prime factors are numbers like 2, 3, 5, and 7. Recall that numbers which are prime can only be evenly divided by the factors of 1 and themselves. This means that all prime numbers only have two factors. For example, the only factors of 7 are 1 and 7.

Review the slides below to learn more about using prime factorization for finding the GCF of a set of numbers.

Factor Trees

One way to find the prime factorization for a number is to create a factor tree. A factor tree organizes the factors of a number visually as you work to having only prime factors.

Let’s factor the numbers 36 and 48.

Factor Tree For 36

Factor tree: Thirty six, three times twelve, three times four, two and two. The Prime factorization for thirty six is three times three times two times two.

Factor Tree For 48

Factor tree: forty eight, four times twelve, two times two, three times four, two times two. The Prime factorization for forty eight is two times two times three times two times two.

What do they have in common?

Compare the prime factorization for both numbers to look for common factors.

Thirty six: two times two times three times three. Forty eight: two times two times three times two times two. Common factors in both numbers are circled together.

36 and 48 share the prime factorization of:
2 x 2 x 3

What is the GCF?

To calculate the GCF, multiply the common prime factors.

36 and 48 share the prime factorization of 2 x 2 x 3. When you multiply 2 x 2 x 3, you get a product of 12.

This means that the GCF of 36 and 48 is 12.

Now you know another strategy you can use to find the GCF of a set of numbers.

Test your new strategy on the number sets below. Find the GCF for each set of numbers using prime factorization.

Eighteen: two times two times three. Forty two: two times three times seven. Common factors in both numbers are circled together.

Multiply: 2 x 3 = 6
The GCF of 18 and 42 is 6.

Fifteen: three times five. Forty five: three times five times three. Common factors in both numbers are circled together.

Multiply: 3 x 5 =15
The GCF of 15 and 45 is 15.

Fifty: two times five times five. Seventy five: three times five times five. Common factors in both numbers are circled together.

Multiply: 5 x 5 = 25
The GCF of 50 and 75 is 25.

Sixty-Three: three times three times seven. Eight one: three times three times three times three. Common factors in both numbers are circled together.

Multiply: 3 x 3 = 9
The GCF of 63 and 81 is 9.