Discussion

Explanation:

14400 = 2⁶ × 3² × 5²

For factor to be odd, the power of 2 should be 0.

∴ Possible power of 2 in factor = 0, i.e., only 1 possibility

There is no restriction of powers of other prime factors.

⇒ The number of odd factors of 14400 = (1)(2 + 1)(2 + 1) = 9

Note: The odd factors of 14400 are 1, 3, 5, 9, 15, 25, 45, 75, 225.

Hence, 9.

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