The number of divisors of 7! is | vedclass

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Question

(D) First,we find the prime factorization of $7!$.$7! = 7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1$$7! = 7 	imes (2 	imes 3) 	imes 5 \

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(D) First,we find the prime factorization of $7!$.$7! = 7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1$$7! = 7 	imes (2 	imes 3) 	imes 5 	imes 2^2 	imes 3 	imes 2 	imes 1$$7! = 2^{1+2+1} 	imes 3^{1+1} 	imes 5^1 	imes 7^1$$7! = 2^4 	imes 3^2 	imes 5^1 	imes 7^1$The number of divisors of a number $N = p_1^{a} 	imes p_2^{b} 	imes p_3^{c} 	imes p_4^{d}$ is given by $(a+1)(b+1)(c+1)(d+1)$.Here,$a=4, b=2, c=1, d=1$.Number of divisors $= (4+1)(2+1)(1+1)(1+1) = 5 	imes 3 	imes 2 	imes 2 = 60$.

The number of divisors of $7!$ is

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