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How many factors of $2^{4} \times 3^{5} \times 7^{2}$ are perfect squares?

Competition practiceNumber System, HCF & LCM

A90
B12
C24
D18

Step-by-Step Solution

A square factor needs even powers:

2^{0, 2, 4}, 3^{0, 2, 4}, 7^{0, 2}

, giving

3 \times 3 \times 2 = 18

.

Answer: D) 18

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