Problem 2 · 2003 AMC 8
Easy
Number Theory
primes
Which of the following numbers has the smallest prime factor?
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Answer: C — 58 (its smallest prime factor is 2).
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Hint 1 of 2
Don't factor all five numbers — ask what the smallest possible prime factor even is, then look for it.
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Hint 2 of 2
The smallest prime is 2, and only even numbers own a factor of 2. Scan for the even one.
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Approach: chase the smallest prime (2) instead of factoring everything
- The winner needs the tiniest prime factor, and no prime beats 2. So the real question is: which choice is even? An even number automatically has 2 as its smallest prime factor.
- 58 is the only even number on the list, so its smallest prime factor is 2 — smaller than any odd number can manage. Answer 58.
- You'll see this again: 'smallest/largest prime factor' problems reward looking for the small primes (2, then 3, then 5) first rather than fully factoring every option.
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