MTTC 103 Elementary Practice

Question: 1 / 400

Which number has a prime factorization of three odd numbers and one even number?

9

21

45

90

A number with a prime factorization that includes three odd numbers and one even number must contain both prime factors that are odd and at least one prime factor that is even. The only even prime number is 2.

In the case of the number 90, its prime factorization is 2 × 3 × 3 × 5. Here, 2 is the even prime factor, while 3 and 5 are the odd prime factors. Specifically, there are three odd numbers in the factorization: two occurrences of 3 and one occurrence of 5.

The other options do not fulfill the requirement of containing one even prime factor and three odd prime factors. For instance, 9 is composed entirely of odd factors (3 × 3), as are 21 (3 × 7) and 45 (3 × 3 × 5). None of these numbers includes an even factor, making 90 the only suitable choice that meets the original condition described in the question.

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