Question

Select the GCF of these numbers.

25 · 5· 11 and 23· 52 · 7

2^2 · 3
2· 11^2
3^2
2^3 ·5
13 · 19^3 ·23^2

Answer 1

Compare the prime factorizations:

25 • 5 • 11 = 5² • 5 • 11 = 5³ • 11

23 • 52 • 7 = 23 • (2² • 13) • 7 = 2² • 7 • 13 • 23

Clearly these products have no common prime factors, so their GCF is 1.

But I'm guessing this a multiple choice question, and the numbers you listed are already prime factorizations. In that case, we have

2⁵ • 5 • 11 = 2³ • 2² • 5 • 11

2³ • 5² • 7 = 2³ • 5 • 5 • 7

with the common factors underlined, so that the GCF is 2³ • 5.