Which of these numbers divides 2^3 × 3^2 × 7 exactly?

24. 24 = 2^3 × 3, and both 2^3 and 3 are inside 2^3 × 3^2 × 7. 16 needs 2^4, 27 needs 3^3 and 49 needs 7^2 — too many of one prime.

Which of these numbers divides $2^{3} \times 3^{2} \times 7$ exactly?

Class 7Prime Factors in Exponent FormNumber System

24 =

2^{3} \times 3

, and both

2^{3}

and 3 are inside

2^{3} \times 3^{2} \times 7

. 16 needs

2^{4}

, 27 needs

3^{3}

and 49 needs

7^{2}

— too many of one prime.

Answer: C) 24

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