What is the number of divisors of n = 38808 ( | vedclass

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(A) First,find the prime factorization of $n = 38808$: $38808 = 8 	imes 4851 = 2^3 	imes 9 	imes 539 = 2^3 	imes 3^2 	imes 7^2 	imes 11^1$. The

Vedclass · Accepted Answer

$70$

Vedclass · Answer

(A) First,find the prime factorization of $n = 38808$: $38808 = 8 	imes 4851 = 2^3 	imes 9 	imes 539 = 2^3 	imes 3^2 	imes 7^2 	imes 11^1$. The total number of divisors is calculated using the formula $(a+1)(b+1)(c+1)(d+1)$ where $a, b, c, d$ are the exponents of the prime factors: Total divisors $= (3+1)(2+1)(2+1)(1+1) = 4 	imes 3 	imes 3 	imes 2 = 72$. Since the question asks for the number of divisors excluding $1$ and $n$,we subtract $2$ from the total: Required number of divisors $= 72 - 2 = 70$.

What is the number of divisors of $n = 38808$ (excluding $1$ and $n$)?

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