Question 117738
The {{{greatest}}}{{{ common}}}{{{ factor}}} of two or more whole numbers is the {{{largest}}}{{{ whole}}}{{{ number}}} that {{{divides}}}{{{ evenly}}} into each of the numbers. 
		

There are {{{two}}} {{{ways}}} to find the greatest common factor. 


The {{{first}}}{{{ method}}} is to list all of the factors of each number, then list the {{{common}}}{{{ factors}}} and choose the {{{largest}}}{{{ one}}}. 


the {{{GCF}}} of {{{105}}} and {{{147}}}:

the factors of {{{105}}} are {{{1}}},{{{ 3}}}, {{{5}}}, {{{7}}}, {{{15}}}, {{{21}}},{{{35}}} and {{{105}}}

thefactors of {{{147}}} are {{{1}}},{{{  3}}},{{{ 7}}},{{{ 21}}},{{{ 49}}} and {{{147}}}

the {{{common}}} factors of {{{105}}} and {{{147}}} are {{{1}}},  {{{3}}},{{{ 7}}},{{{ 21}}}

Although the numbers in bold are all common factors of both {{{105}}} and {{{147}}}, {{{21}}} is the greatest common factor.

The {{{second}}}{{{ method}}} for finding the greatest common factor is:

 to list the{{{ prime }}}{{{factors}}}, then {{{multiply}}} the {{{common}}}{{{ prime}}}{{{ factors}}}
 
The prime factorization of {{{105}}} and {{{147}}} is:
{{{105 =3*5*7}}}

{{{147=3*7*7}}}

Notice that the prime factorizations of {{{105}}} and {{{147}}} both have one{{{ 3}}} and one {{{7}}} in common. 

So, we simply {{{multiply}}} these common prime factors to find the greatest common factor:
 {{{3 *7= 21}}}
	
so, correct answer is: a) {{{21 }}}