Number Properties : How to find the number of factors?

The question a Number Properties question and is about finding the number of factors of a positive integer.

Question

How many different factors does 48 have, excluding 1 and 48?

1. 12
2. 4
3. 8
4. 10
5. None of these

Correct Answer - 8. Choice (3)

Explanatory Answer

One of the ways to solve this question is by listing all factors of 48 and then counting them after excluding 1 and 48.

The factors of 48 : 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

48 has a total of 10 factors including 1 and 48.
Therefore, 48 has 8 factors excluding 1 and 48.

Alternative Method

To find the number of factors of a given number, express the number as a product of powers of prime numbers.

In this case, 48 can be written as 16 * 3 = (2⁴ * 3)

Now, increment the power of each of the prime numbers by 1 and multiply the result.

In this case it will be (4 + 1) * (1 + 1) = 5 * 2 = 10 (the power of 2 is 4 and the power of 3 is 1)

Therefore, there will 10 factors including 1 and 48.

Excluding, these two numbers, you will have 10 - 2 = 8 factors.

Correct answer choice (3)

Level of difficulty : Moderate

---

More Questions Answers on Number Theory

CAT, XAT, TANCET Practice Questions and Answers : Listed Topicwise

Number Theory		Permutation Combination		Probability		Inequalities
Geometry		Mensuration		Trigonometry		Coordinate Geometry
Percentages		Profit Loss		Ratio Proportion		Mixtures Alligation
Speed Time Distance		Pipes Cisterns		Interest		Races
Average, Mean		AP, GP, HP		Set Theory		Clocks Calendars
Algebra		Function		English Grammar		General Awareness
Data sufficiency		TANCET Papers		XAT Papers