If a, b, c, d, e are prime integers,then the | vedclass

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

Question

(D) The given number is $N = a^1 b^2 c^2 d^1 e^1$.Since $a, b, c, d, e$ are prime integers,the total number of divisors of $N$ is given by the product

Vedclass · Accepted Answer

$71$

Vedclass · Answer

(D) The given number is $N = a^1 b^2 c^2 d^1 e^1$.Since $a, b, c, d, e$ are prime integers,the total number of divisors of $N$ is given by the product of (exponent + $1$) for each prime factor.Total number of divisors $= (1 + 1)(2 + 1)(2 + 1)(1 + 1)(1 + 1) = 2 	imes 3 	imes 3 	imes 2 	imes 2 = 72$.We need to find the number of divisors excluding $1$ as a factor.Number of divisors excluding $1 = 72 - 1 = 71$.

If $a, b, c, d, e$ are prime integers,then the number of divisors of $a b^2 c^2 d e$ excluding $1$ as a factor is:

Similar Questions

The sum of the divisors of $2^5 \times 3^4 \times 5^2$ is

The number of natural number solutions to the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to

The smallest positive divisor greater than $1$ of a composite number $a$ is

Let $f(x) = 2x^n + \lambda$,where $\lambda \in R$ and $n \in N$. Given $f(4) = 133$ and $f(5) = 255$,find the sum of all the positive integer divisors of $(f(3) - f(2))$.

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module