CAT Quantitative Aptitude Questions | CAT Number Systems - Factors

The question is about perfect square factors. A number is given. 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. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

Question 2: How many factors of 1080 are perfect squares?

1. 4
2. 6
3. 8
4. 5

Explanatory Answer

Method of solving this CAT Question from Number Theory - Factors: We know how to find number of factors of a number. How do you find the number of factors that are perfect squares?

1080 = 2³ * 3³ * 5. For any perfect square, all the powers of the primes have to be even numbers. So, if the factor is of the form 2^a * 3^b * 5^c.
The values 'a' can take are 0 and 2, b can take are 0 and 2, and c can take the value 0.
Totally there are 4 possibilities. 1, 4, 9, and 36.

The question is "How many factors of 1080 are perfect squares?"

Hence the answer is 4.

Choice A is the correct answer.