JIPMAT 2023 (QA) - <p>How many proper divisors (that is, divisors other than 1 or 7200) does 7200 have?</p> | PYQs + Solutions

JIPMAT 2023

Number System

Factorisation

Easy

How many proper divisors (that is, divisors other than 1 or 7200) does 7200 have?

Correct Option: 2

To find the number of factors of a number

N = p^{a} × q^{b} × r^{c}

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The formula is:

(a+1)(b+1)(c+1)

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where

a,b,c

are powers in prime factorization and

p,q,r

are prime numbers

For 7200:

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Prime factorization =

2^5 × 3^2 × 5^2

Total number of factors:

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(5+1)(2+1)(2+1)

= 6 × 3 × 3

= 54

factors

Proper divisors exclude 1 and the number itself

Therefore, number of proper divisors =

54 - 2 = 52

The answer is

52.