Factoring Numerical Expressions using GCF
Factoring a numerical expression using the GCF reverses the distributive property: find the GCF of all terms, then rewrite the expression as GCF times the sum of the remaining factors. For 12 + 18: GCF is 6, so 12 + 18 = 6(2 + 3). For 24 + 36: GCF is 12, so 24 + 36 = 12(2 + 3). This technique from Reveal Math, Course 1, Module 5 is the algebraic inverse of distribution and builds the foundation for factoring variable expressions in 6th grade math.
Key Concepts
Property To factor a numerical expression, find the greatest common factor (GCF) of the terms. Then use the distributive property in reverse to write the expression as the GCF multiplied by a sum of the remaining factors. The general form is $ab + ac = a(b+c)$, where $a$ is the GCF.
Examples To factor $12 + 18$, the GCF of $12$ and $18$ is $6$. So, $12 + 18 = 6(2) + 6(3) = 6(2+3)$. To factor $35 + 50$, the GCF of $35$ and $50$ is $5$. So, $35 + 50 = 5(7) + 5(10) = 5(7+10)$. To factor $24 + 36$, the GCF of $24$ and $36$ is $12$. So, $24 + 36 = 12(2) + 12(3) = 12(2+3)$.
Explanation Factoring a numerical expression is the opposite of expanding it. First, identify the greatest common factor (GCF) of the numbers in the sum. Then, you "pull out" the GCF and write the remaining factors inside parentheses. This process rewrites a sum as a product, which is a key application of the distributive property.
Common Questions
How do I factor a numerical expression using the GCF?
Find the GCF of all terms. Divide each term by the GCF to find what goes inside the parentheses. Write the factored form as GCF times the sum of those remaining factors.
Factor 12 + 18 using the GCF.
GCF of 12 and 18 is 6. Divide: 12 divided by 6 = 2 and 18 divided by 6 = 3. Factored form: 6(2 + 3).
Factor 35 + 50 using the GCF.
GCF of 35 and 50 is 5. Divide: 35/5 = 7 and 50/5 = 10. Factored form: 5(7 + 10).
How is factoring with GCF related to the distributive property?
Factoring is the reverse of distribution. Distributing means 6(2 + 3) = 12 + 18. Factoring means 12 + 18 = 6(2 + 3). One expands, the other compresses.
How do I check that my factoring is correct?
Distribute your answer back out. If 6(2 + 3) = 12 + 18, then your factoring is correct.
When do 6th graders learn to factor with GCF?
Module 5 of Reveal Math, Course 1 covers factoring numerical expressions in the Numerical and Algebraic Expressions unit.