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Find the smallest composite number that has no prime factors less than \(20\).

 May 12, 2022
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Consider the prime factorization of the answer. The factorization cannot contain primes smaller than 20.

That means all prime factors must be greater than or equal to 20.

The smallest prime greater than or equal to 20 is 23.

Since it cannot be just 23 (it would be a prime, not a composite number), we arrive at the conclusion that \(23^2 = 529\) is the smallest composite number that has no prime factors less than 20.

 May 12, 2022

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