Problem 3 · 2007 AMC 8
Easy
Number Theory
prime-factorization
What is the sum of the two smallest prime factors of 250?
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Answer: C — 7.
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Hint 1 of 2
250 ends in 0, so it's even and a multiple of 5 — you already know its two smallest primes without dividing anything.
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Hint 2 of 2
The smallest prime factors hide in the last digit: even ⇒ 2 lives there; ending in 0 or 5 ⇒ 5 lives there.
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Approach: spot the primes from the last digit
- 250 ends in 0, which means it's divisible by both 2 and by 5 — the two smallest primes any number can have. So the two smallest are 2 and 5 with no work.
- Sum: 2 + 5 = 7.
- Why you can stop: 2 and 5 are the smallest two primes that exist, so once a number has both, nothing smaller can sneak in. (Fully, 250 = 2 · 53, but you never needed that.)
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