# Factors of 48

The factors of 48 are the numbers that completely divide 48 without leaving a remainder. Thus we can say that the factors of 48 are the divisors of 48. In this section, we will learn about the factors of 48 and the prime factors of 48.

## Highlights of Factors of 48

• 48 = 2×2×2×2×3 = 24×3 is the prime factorization of 48.
• The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
• 2 and 3 are the prime factors of 48.
• The negative factors of 48 are -1, -2, -3, -4, -6, -8, -12, -16, -24, and -48.

## What are the factors of 48?

To find the factors of 48 by the multiplication method, we need to write the number 48 multiplicatively in all possible ways. Note that we can write 48 as follows and we have:

As there are no other ways we can express 48 multiplicatively, we will stop now.

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

Note that the negative of a positive factor of 48 is a negative factor of 48. So the negative factors of 48 are -1, -2, -3, -4, -6, -8, -12, -16, -24, and -48.

## Pair Factors of 48

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

Now, the negative pair factors of 48 are obtained by the fact: (a, b) is a positive factor of 48 if and only if (-a, -b) is a negative factor of 48. So the negative pair factors of 48 are (-1, -48), (-2, -24), (-3, -16), (-4, -12), and (-6, -8).

## Number of factors of 48

From above we see that the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Thus the total number of factors of 48 is ten.

## Prime Factors of 48

We have found above that the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 48 are 2 and 3.

Question: What are the factors of 48?

Video Solution:

## Factors of -48

Factors of negative 48: The factors of -48 are the same as the factors of 48. It includes both the positive and negative factors of 48. So the factors of negative 48 are  1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, and -48.

## How to find Factors of 48?

By division method, we will determine the factors of 48. In this method, we will find the numbers that can divide 48 completely with the remainder zero. See that

Note that no numbers other than the numbers in violet color can divide 48. So the numbers in violet color, that is, 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 are the complete list of factors of 48.