Discussion

Explanation:

14400 = 2⁶ × 3² × 5²

For factor to be even, the least power of 2 should be 1.

∴ Possible power of 2 in factor = 1 or 2 … or 6, i.e., 6 possibilities

There is no restriction of powers of other prime factors.

⇒ The number of even factors of 14400 = (6)(2 + 1)(2 + 1) = 54

Hence, 54.

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