CAT Quantitative Aptitude Questions | CAT Number Systems - Factors

The question is about Odd Factors. A number is given as multiplication of prime factors. We need to find out the number of odd 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 4: How many factors of 2⁴ * 5³ * 7⁴ are odd numbers?

1. 100
2. 99
3. 20
4. 24

Explanatory Answer

Method of solving this CAT Question from Number Theory - Factors: How many factors does a number have? That's a straightforward qn. How many factors of a number are odd; now that's an interesting variant.

Any factor of this number should be of the form 2^a * 5^b * 7^c.
For the factor to be an odd number,
a should be 0.
b can take values 0, 1, 2, 3.
and c can take values 0, 1, 2, 3, 4.
Total number of odd factors = 4 * 5 = 20.

The question is "How many factors of 2⁴ * 5³ * 7⁴ are odd numbers?"

Hence the answer is 20

Choice C is the correct answer.