# 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?

- 12
- 4
- 8
- 10
- 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 = (2

^{4} * 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

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