CAT Quantitative Aptitude Questions | CAT Number Systems - Factors

The question is about perfect square factors. A number is given as multiplication of prime factors. We need to find out the number of perfect square factors of that number. Dealing with factors of a number is a vital component in CAT Number Systems: Factors. A range of CAT questions can be asked based on this simple concept of Factors. CAT exam has always tested the idea of Factors from Number systems. The idea of Factors questions forms an integral part of the CAT syllabus.

Question 3: How many factors of 2⁵ * 3⁶ * 5² are perfect squares?

1. 18
2. 24
3. 36
4. 8

Explanatory Answer

Method of solving this CAT Question from Number Theory - Factors: Given a prime factorization, how do we find how many factors of the number are perfect squares.

Any factor of this number should be of the form 2^a * 3^b * 5^c.
For the factor to be a perfect square a,b,c have to be even.
a can take values 0, 2, 4.
b can take values 0, 2, 4, 6
and c can take values 0, 2
Total number of perfect squares = 3 * 4 * 2 = 24

The question is "How many factors of 2⁵ * 3⁶ * 5² are perfect squares?"

Hence the answer is 24.

Choice B is the correct answer.