Question

Find the greatest common factor of 8a 3 b 2 and 12ab 4.

Answer 1

`2^(2) * a * b^(2)=4ab^(2)`

Explanation:

Greatest common factor of two or more terms is the largest(greatest) possible term which exactly divides all the given term. For example the greatest common factor of 20 and 30 is 10 as 10 is the largest possible number that can exactly divide 20 and 30 without leaving any remainder. GCF is found as the product of all the common factors

Given terms are:

`8a^(3) b^(2) =2^(3)* a^(3)* b^(2)`

`12ab^(4)=4 * 3 ab^(4) =2^(2) * 3 * a * b^(4)`

From the above factors we can see that the common factors are:

`2^(2) , a , b^(2)`

Therefore, the greatest common factor will be:

`GCF=2^(2) * a * b^(2)=4ab^(2)`