What is the greatest common factor for each of the following 
groups of numbers: 
36, 72 and 144

Break each down into a product of prime factors:

36 = 4·9 = 2·2·3·3 

72 = 8·9 = 2·4·3·3 = 2·2·2·3·3

144 = 16·9 = 4·4·3·3 = 2·2·2·2·3·3

 36 has 2 factors of 2 and 2 factors of 3
 72 has 3 factors of 2 and 2 factors of 3
144 has 4 factors of 2 and 2 factors of 3 

To find the GREATEST COMMON FACTOR, use the LEAST number of 
each factor that is common to all.

The factor 2 is common to all, and the least number of 2's is 2,
so use 2 2's

The factor 3 is common to all, and the least number of 3's is 2,
so use 2 3's

So the GCF has 2 2's and 2 3's or

2·2·3·3 = 36

GCF = 36

Edwin
AnlytcPhil@aol.com