The number of divisors of n = 38808,excluding | vedclass

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Question

(A) First,find the prime factorization of $38808$: $38808 = 8 	imes 4851 = 8 	imes 9 	imes 539 = 8 	imes 9 	imes 7 	imes 77 = 8 	imes 9 	imes

Vedclass · Accepted Answer

$70$

Vedclass · Answer

(A) First,find the prime factorization of $38808$: $38808 = 8 	imes 4851 = 8 	imes 9 	imes 539 = 8 	imes 9 	imes 7 	imes 77 = 8 	imes 9 	imes 7 	imes 7 	imes 11 = 2^3 	imes 3^2 	imes 7^2 	imes 11^1$. The total number of divisors is given by the product of (exponent + $1$) for each prime factor: Total divisors = $(3+1)(2+1)(2+1)(1+1) = 4 	imes 3 	imes 3 	imes 2 = 72$. Since we must exclude $1$ and $n$ (the number itself),we subtract $2$ from the total count: Number of divisors excluding $1$ and $n$ = $72 - 2 = 70$.

The number of divisors of $n = 38808$,excluding $1$ and $n$,is ....

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