Which of these are prime numbers: 2, 3, 4, 5, 6, 31, 32, 33? What are 42 and 24 as the products of their prime factors?

2, 3, 5, and 31 are prime numbers.

The others all have factors:

4 = 2 × 2,

6 = 2 × 3,

32 = 2 × 2 × 2 × 2 × 2,

33 = 3 × 11.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Of these 2, 3, and 7 are primes greater than 1. As a product of its prime factors,

42 = 2 × 3 × 7

None of the factors appears more than once.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Of these, only 2 and 3 are primes greater than 1. However, 2 × 3 = 6, not 24, so these prime factors must appear more than once. As the product of its prime factors,

24 = 2 × 2 × 2 × 3

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Last updated: 9 October, 2007.