Greatest Common Factor Sample Problems

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Here are some tips for Greatest Common Factor, which aligns with New York state standards:

Greatest Common Factor

To review factoring, see here.

To find the greatest common factor, you need to figure out all of the factors and then simply pick the largest one.

Example 1: Find the GCF of 16 and 24
Factors of 16: 1,2,4,8,16
Factors of 24: 1,2,3,4,6,8,12,24
The greatest common factor is 8.

Important Tip Listing all of the factors and then picking the largest one is very time consuming. Instead, you should pull out all of the common prime factors.

Example 2: Find the GCF of 16 and 24
Prime Factors of 16: 2*2*2*2
Prime Factors of 24: 2*2*2*3
The greatest common factor is 2*2*2=8

This technique is much faster than the technique used in example 1. If you want to excel, use this technique.

Advanced Tip (Don't worry if you don't understand it): Take the difference of the two numbers to obtain a third number. The lowest number is the highest possible value that could be the GCF. Also, the GCF of the two lowest numbers is the GCF of the original two numbers.

Example 3: Find the GCF of 48 and 64
The difference is 64 - 48 = 16. (16 is the third number as mentioned in the tip)
Does 16 go into 48? Yes, so the GCF is 16.

Example 4: Find the GCF of 91 and 77
91 - 77 = 14
Does 14 go into 77? no
What are the prime factors of 14? 2 and 7
Does 2 go into 77? no
Does 7 go into 77? yes
Therefore, the GCF of 91 and 77 is 7.