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In the division ladder for 360, one divisor is hidden. What is 360 as a product of powers of primes?

Class 7Prime Factors in Exponent FormNumber System

A $2^{3} \times 3 \times 5$
B $2^{3} \times 3^{2} \times 5^{2}$
C $2^{3} \times 3^{2} \times 5$
D $2^{2} \times 3^{2} \times 5$

Step-by-Step Solution

The hidden divisor takes 15 to 5, so it is 3. The divisors are 2, 2, 2, 3, 3, 5, giving

360 = 2^{3} \times 3^{2} \times 5 (8 \times 9 \times 5 = 360)

.

Answer: C)

2^{3} \times 3^{2} \times 5

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