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

The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ 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

Three players play a total of $9$ games. In each game,one person wins and the other two lose; the winner gets $2$ points and the losers get $-1$ each. The number of ways in which they can play all the $9$ games and finish each with a zero score is

The sum of the divisors of $9000$ is . . . . . . .

The coefficient of $a^{10} b^7 c^3$ in the expansion of $(bc + ca + ab)^{10}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module