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

Expert Answers
lfryerda eNotes educator| Certified Educator

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:

`5/18+13/27`

`=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

`=41/54`

The GCF can be used to simplify adding two fractions.