can u give me example proble of simplify GCF and solve it step by step

1 Answer

lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted on

The GCF is the greatest common factor of two numbers.  We usually use GCF when adding fractions or simplifying some numerical expressions.

Consider adding the two fractions together:

`5/18+13/27`   to simplify this, we get the GCF of 18 and 27

If we factor 18, we see that it can be written as

`18=1 times 18`

`18=2times 9`

`18=3 times 6`

and factoring 27, we get

`27 = 1 times 27`

`27 = 3 times 9`

The GCF is the largest factor that is the same between those lists of factors.  In this case, the GCF is 9.  Now rewrite the fractions using GCF:


`=5/{(2)(9)}+13/{(3)(9)}`   now get common divisors using the 2 and 3

`={5(3)+13(2)}/{(2)(3)(9)}`   then simplify the numerator

`={15+26}/{(2)(3)(9)}`  keep simplifying the numerator


The GCF can be used to simplify adding two fractions.