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A number that is a perfect square has an odd number of factors. A number that is a 4th power has an odd number of factors. The same holds for other even-numbered powers.

The factors of 4 = 22 are 1, 2, and 4.

The factors of 9 = 32 are 1, 3, and 9.

The factors of 16 = 42 = 24 are 1, 2, 4, 8, and 16.

The factors of 25 = 52 are 1, 5, and 25.

The factors of 36 = 62 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The factors of 49 = 72 are 1, 7, and 49.

The factors of 64 = 82 = 26 are 1, 2, 4, 8, 16, 32, and 64.

The factors of 81 = 92 = 34 are 1, 3, 9, 27, and 81.

The factors of 100 = 102 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

The factors of 144 = 122 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

The factors of 256 = 162 = 44 = 28 are 1, 2, 4, 8, 16, 32, 64, 128, and 256.

The factors of 1024 = 322 = 210 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024.

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14y ago

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