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
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