Number of divisors and Integers | TOMATO B.Stat Objective 97

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

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.