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16! has 5,376 factors.

16! = 16 x 15 x 14 x 13 x 12 x 11 x10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

→ 16! = (2^4) x (3 x 5) x (2 x 7) x 13 x (2^2 x 3) x 11 x (2 x 5) x (3^2) x (2^3) x 7 x (2 x 3) x 5 x (2^2) x 3 x 2

→ 16! = 2^15 x 3^6 x 5^3 x 7^2 x 11^1 x 13^1

→ number of factors = (15 + 1) x (6 + 1) x (3 + 1) x (2 + 1) x (1 + 1) x (1 + 1) = 16 x 7 x 4 x 3 x 2 x 2 = 5,376.

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βˆ™ 10y ago
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Q: How many factors does the number 16 factorial have?
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