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How many positive divisors does 10! have?

Competition practiceNumber System, HCF & LCM

A270
B240
C256
D300

Step-by-Step Solution

10! =

2^{8} \times 3^{4} \times 5^{2} \times 7

. Number of divisors =

(8 + 1) (4 + 1) (2 + 1) (1 + 1) = 9 \times 5 \times 3 \times 2 = 270

.

Answer: A) 270

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