# Factors Of 48 – With Division and Prime Factorization

## Factors Of 48

Numbers that divide 48 fully, leaving zero as a remainder, are its factors. In other words, they are the numbers that multiply 48 together in pairs, or we can say that they are the numbers that divide 48 completely, leaving zero as a remainder. There are positive and negative factors of 48.

In the case of 48, the factors can be (1, 48) or (-1, -48). When we multiply one negative factor by another, such as multiplying -1 by -48, we get 48.

By using the prime factorization method, here we will learn the factors of 48, the pair factors, and the prime factors of 48.

## What are the Factors of 48?

Numbers dividing 48 exactly without leaving a remainder are the factors of 48. Hence, the factors of 48 are the numbers multiplied in pairs to result in an original number.

The number 48 has many factors other than 1 and 48 since it is an even composite number. As a result, 48 has the factors 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

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

Prime Factorization of 48: 2×2×2×2×3 or 24 × 3.

## What are the Factors Of -48?

Factors of -48: -1, -2, -3, -4, -6, -8, -12, -16, -24 and -48.

When we multiply two numbers to get -48, it comes out as follows:

-1 x  48 =  -48     &   1 x -48 =  -48

-2 x  24 =  -48     &  2 x  -24 =  -48

-3 x  16 = -60      &  3 x  -16 =  -48

-12 x  4 =  -48     &  12 x  -4 =  -48

-8 x  6 = -60         &      8 x  -6 =  -48

## Pair Factors of 48

When two numbers are multiplied together, the result is the original number 48. 48 may also have positive or negative pair factors, as discussed above.

Accordingly, the positive and negative pair factors of 48 are as follows:

Positive Pair Factors of 48:

Negative Pair Factors of 48:

## Factors of 48 by Division Method

Divide 48 by consecutive integers to find the factors of 48 with the division method. Integers that divide 48 exactly and leave the remainder 0 are factors of 48. We will now discuss how to find the factors of the division method.

• 48/1 = 48
• 48/2 = 24
• 48/3 = 16
• 48/4 = 12
• 48/6 = 8
• 48/8 =6
• 48/12 = 4
• 48/16 = 3
• 48/48 = 1

Accordingly, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

When we divide 48 by any number other than 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, a remainder is left, and so these numbers are not factors of 48.

## Prime Factorization of 48

In math, 48 is a composite number. Now let’s determine its prime factorization.

First, we must divide 48 by the smallest prime factor, i.e. 2.

48 ÷ 2 = 24

Try to divide 24 by 2 now.

24 ÷ 2 = 12

12 ÷ 2 = 6

6 ÷ 2 = 3

The factor 3 cannot be divided by 2 since factors are whole numbers, not fractions.

Since 3 is the next prime number, we must divide it by 3.

3 ÷ 3 = 1

Since we have received 1 at the end, we are unable to divide.

Consequently, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or 24× 3 where 2 and 3 are both prime numbers.

## Examples

Example 1:

Calculate the common factors of 48 and 47.

Solution:

Factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

47 has two factors: 1 and 47.

Since 47 is a prime number, the common factor of 47 and 48 is 1.

Example 2:

Calculate the common factors of 48 and 49.

Solution:

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

There are three factors of 49: 1, 7, and 49.

Therefore, 48 and 49 have a common factor of 1.

Example 3:

Find the common factor between 48 and 24.

Solution:

48 has the following factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

24 has the factors 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore, 48 and 24 have the same common factors of 1, 2, 3, 4, 6, 8, 12 and 24

## FAQs

### How many factors are there in 48?

Factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

### What is the prime factorization of 48?

In prime factorization, 48 is 2×2×2×2×3 or 24 × 3.

### What are the positive pair factors of 48?

For 48, the positive pair factors are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).

### How many negative pair factors are there in 48?

Negative pair factors of 48 are (-1, -48), (-2, -24), (-3, 16), (-4, 12), and (-6, 8).

### Is 24 a factor of 48?

24 is a factor of 48, yes. 24 is a factor of 48 because when 48 is divided by 24, there is no remainder.