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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 ....

Similar Questions

For any integer $n \geq 1$,the number of positive divisors of $n$ is denoted by $d(n)$. Then,for a prime $P$,$d(d(d(P^7)))$ is equal to

The digit in the unit place of the number $843^{843} + 492^{295}$ is:

The coefficient of $x^{1012}$ in the expansion of $(1 + x^n + x^{253})^{10}$,where $n \leq 22$ is any positive integer,is

$A$ natural number $n$ such that $n!$ ends in exactly $1000$ zeros is

The number $111...1$ ($91$ times) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module