The number of odd proper divisors of 3p6m21n is | MATH - DEFINITON OF COMBINATIONS, CONDITION COMBINATIONS, DIVISION INTO GROUPS, DERANGEMENTS | SolveeIt | Solveeit

Today, August 19

Question

The number of odd proper divisors of 3^p6^m21ⁿ is

A

(p + 1) (n + 1) (m + 1) – 2

B

(p + m + n + 1) (n + 1) – 1

C

(p + 1) (m + 1) (n + 1) – 1

D

pmn – 2

Answer

(p + m + n + 1) (n + 1) – 1

Explanation

Solution

3^p 6^m 21ⁿ = 3^{p + m + n} 2^m 7ⁿ

The number of odd factors of the given number.

= (p + m + n + 1) (n + 1) – 1

(considering only zero power of 2).