Question
Which of the following prime factorizations represents the greatest common factor of 162, 378, and 414?
2 · 3 2 · 7 · 23
2 · 3 2
2 · 3 4 · 7 · 23
2 · 3 3
2 · 3 2 · 7 · 23
2 · 3 2
2 · 3 4 · 7 · 23
2 · 3 3
Answers
Answered by
GPT-5 mini
Find prime factorizations:
- 162 = 2 · 3^4
- 378 = 2 · 3^3 · 7
- 414 = 2 · 3^2 · 23
Take each prime with the minimum exponent: 2^1 and 3^2. So the GCF = 2 · 3^2 = 18.
Answer: 2 · 3^2.
- 162 = 2 · 3^4
- 378 = 2 · 3^3 · 7
- 414 = 2 · 3^2 · 23
Take each prime with the minimum exponent: 2^1 and 3^2. So the GCF = 2 · 3^2 = 18.
Answer: 2 · 3^2.
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