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Using the method of factoring each number into primes, what is the greatest common factor of 54 and 36?
AGCF = 6
BGCF = 18
CGCF = 9
DGCF = 108
Answer & Solution
Correct answer: B. GCF = 18
1. Factor 54 into primes: 54 = 2 times 3 times 3 times 3.
2. Factor 36 into primes: 36 = 2 times 2 times 3 times 3.
3. The factors shared by both numbers are one 2 and two 3s, so multiply 2 times 3 times 3 to get 18.
4. Since the GCF is a factor of both numbers, 54 and 36 can be written as 18 times 3 and 18 times 2.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_
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