2007 AMC 8 Problem 3

Attempt Problem 3 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

What is the sum of the two smallest prime factors of 250?250?
22
55
77
1010
1212
Answer: C
Concepts:prime factorization
Small hint:
Factor 250250 into primes.
Big hint:
Only distinct prime factors matter when looking for the two smallest prime factors.
Solution:
We can prime factorize 250250 to get 250=2⋅53. 250 = 2 \cdot 5^3. From this, we can see that 250250 only has two prime factors: 22 and 5.5. The sum of these is 7.7.
Thus, C is the correct answer.
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