Example: 30 and 42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
or
The factors of 30 are:
1, 2, 3, 5, 6, 10, 15, 30
The factors of 42 are:
1, 2, 3, 6, 7, 14, 21, 42
The common factors are:
1, 2, 3, 6
The Greatest Common Factor:
GCF = 6
Euclid is the Greek mathematician who invented an easier way of finding the GCF.
Yes there is
It is preferable because this is the purpose, the ultimate aim, of simplification. You can only simplify to the extent that the greatest common factor will allow. You can do so in one step by finding the greatest common factor, or you can do so in multiple steps by first dividing by a lower factor (when you are finished you will see that all the lower factors multiply to give the gcf). Sometimes it is easier to do the task in multiple steps rather than searching for the gcf, but if you can identify the gcf then your simplification will be done in just one step.
Yes.
There are a few steps to rewriting expressions. The steps of rewriting expressions are finding the value of the letter and then using the common factor.