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Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Number of divisors and Integers.

## Number of divisors and Integers (B.Stat Objective Question)

The number of different factors of 6000, where 1 and 6000 are also considered as divisors of 6000, is

• 104
• 40
• 1154
• none of these

### Key Concepts

Integers

Number of divisors

Exponents

But try the problem first…

Source

B.Stat Objective Problem 97

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

Here 6000=(2)(2)(2)(2)(3)(5)(5)(5)

Second Hint

number of divisors of 6000 =(4+1)(1+1)(3+1) where number of divisors=(a+1)(b+1)(c+1) for n=$p_1^{a}p_2^{b}p_3^{c}$ as $p_1,p_2,p_3$ are primes

Final Step

=(5)(2)(4)=40.