Exercise 554Number theory › PrimesHigh schoolAdded 3 Nov 2026

The smallest prime factor

#smallest prime factor#compositeness#bounds

Statement

For $n=1001$ , find the smallest prime factor and check the primality test bound.

Hint

$\sqrt{1001}\approx31.6$ , so test primes up to $31$ .

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Test primes. $2,3,5$ don't divide $1001$ . $7\mid1001$ .

Smallest. $7$ .

Bound check. $7\le31.6$ , consistent.

Conclusion. The smallest prime factor is $7$ ; testing up to $\sqrt{1001}$ was sufficient.