Greatest Common Factor

and the Distributive Property

You previously learned about the distributive property, but in case you have forgotten about it…

Given two terms, the first being a number and the second the sum of two numbers, the product of the two terms is the same as the sum when multiplying each of the addends by the first term.

Example: 5(4 + 3) =

You can use the distributive property in combination with the concept of GCF to re-write multiplication expressions.

Greatest Common Factor

5 • 4 + 5 • 3

Example 1: Express the sum of 15 and 25 as the product of the GCF and the sum of their respective factors.  First, find the GCF of 15 and 25: _____ 

Next, write the GCF as the term outside the parenthesis:__ ( __ + __ )

 Finally, write the factor that when multiplied by the term outside the parenthesis will give you the original numbers. __ ( __ + __ )

How To…

55

5 3 4

Example 2: Express the sum of 36 and 66 as the product of the GCF and the sum of their respective factors.  First, find the GCF of 36 and 66: _____ 

Next, write the GCF as the term outside the parenthesis:__ ( __ + __ )

 Finally, write the factor that when multiplied by the term outside the parenthesis will give you the original numbers. __ ( __ + __ )

How To…

66

6 6 11

Example 1: Express the sum of 16 and 64 as the product of the GCF and the sum of their respective factors.  First, find the GCF of 36 and 66: _____ 

Next, write the GCF as the term outside the parenthesis:__ ( __ + __ )

 Finally, write the factor that when multiplied by the term outside the parenthesis will give you the original numbers. __ ( __ + __ )

More Examples

1616

16

1 4

Example 1: Express the sum of 32 and 96 as the product of the GCF and the sum of their respective factors.  First, find the GCF of 32 and 96: _____ 

Next, write the GCF as the term outside the parenthesis:__ ( __ + __ )

 Finally, write the factor that when multiplied by the term outside the parenthesis will give you the original numbers. __ ( __ + __ )

More Examples

3232

32

1 3