One number has a prime factorization of 2 3 · 3 2, and another number has a prime factorization of 2 2 · 3 3. Which of the following expressions would equal the greatest common factor of these two numbers?
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Given : One number has a prime factorization of 2³ · 3² , and another number has a prime factorization of 2² · 3³.
To Find : the greatest common factor of these two numbers
Solution:
prime factorization of one number = 2³ · 3²
prime factorization of another number = 2² · 3³
2³ · 3² = 2.2² · 3²
2² · 3³ = 3..2² · 3²
2² · 3² is the greatest common factor of these two numbers
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