First slide

Combinations

Question

The number of divisors a number 38808 can have, excluding 1 and the number itself is

Moderate

A

70
B

72
C

71
D

None of these

Solution

Factorizing the given number, we have
$38808 = 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11$
Therefore, the total number of divisors = (3 +1) (2 + 1) (1 + 1) – 1 = 71.
But this includes the division by the number itself.
Hence, the required number of divisors = 71 – 1 = 70.

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