# Factors of 52

Factors of 52 are the numbers that are multiplied in pairs to give the product value as 52. The pair factors of 52 can be positive as well as negative. For example, the pair factor of 52 is (1, 52) and (-1, -52). If we multiply the pair of negative factors, such as multiplying -1 and -52, it will result in the original number 52. In this article, we will learn what are the factors of 52, pair factors and the prime factors of 52, and steps to find the factors of 52, using the prime factorization method with many solved examples.

## What are the Factors of 52?

We know that the factors of a number are the number that divides the original number completely without leaving any remainder. Thus, the factors of 52 are the numbers that are multiplied in pairs resulting in the original number 52. The number 52 is a composite number and it has many factors other than one and the number itself.

 Factors of 52: 1, 2, 4, 13, 26, and 52. Prime Factorization of 52: 22 × 13

## How to Find the Prime Factors of 52?

Go through the following steps to find the factors of 52. They are:

Step 1: Write down the number, which has to be factorized.

Step 2: Find two numbers, whose product is equal to the original number.

For example, let us take two factors, say 2 and 26 to be a factor of number 52.

From the two numbers, 2 is a prime number and hence it cannot be factored further.

Now, take the number 26, which is a composite number.

Thus, 26 can be further split as the product of 2 and 13.

Hence, 52 is written as the product of 2, 2 and 13.

It means that 52 can be written as 2 × 2 × 13 = 4 × 13 = 52.

## Pair Factors of 52

If the multiplication of a pair of numbers results in the number 52, then it is called the pair factor of 52. The pair factors of 52 can be written in the positive as well as in the negative pairs. The following are the positive pair factors of 52.

 Positive Factors of 52 Positive Pair Factors of 52 1 × 52 (1, 52) 2 × 26 (2, 26) 4 × 13 (4, 13)

Similarly, the negative pair factors of 52 are as follows:

 Negative Factors of 52 Negative Pair Factors of 52 -1 × -52 (-1, -52) -2 × -26 (-2, -26) -4 × -13 (-4, -13)

Note:

• The pair factors of 52 can be negative as well.
• The factors of 52 can neither be decimals nor fractions.

## Prime Factorization of 52

The prime factorization method is the process of writing the number as the product of its prime factors. The following steps help to find the factors of 52 using the prime factorization method.

Step 1: Write down the pair factors of 52, which on multiplication gives the original number 52.

Step 2: Determine whether the factors of 52 are a prime number or a composite number.

If both the factors of 52 are prime numbers, then multiply the factor pair directly.

If one of the factors of 52 is prime and the other factor is composite, split the composite factor further and make it a prime factor, and multiply the prime factors together.

If both the factors of 52 are composite numbers, then split both the composite factors further into the prime factors, and multiply the prime factors.

Now, let us learn how to find the prime factors of 52 using the prime factorization method.

Consider the pair factor of 52, (4, 13)

From the pair factor (4, 13), 13 is a prime factor, and leave the number as it is.

Now, consider the other factor 4, which is composite and it can be factored as the product of 2 and 2.

Hence, 52 is written as 2 × 2 × 13

Therefore, the prime factorization of 52 is 2 × 2 × 13 or 22 × 13.

### Examples

Example 1:

Find the common factors of 52 and 36.

Solution:

The factors of 52 are 1, 2, 4, 13, 26 and 52

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

Thus, the common factors of 52 and 36 are 1, 2 and 4.

Example 2:

Find the common factors of 52 and 48.

Solution:

Factors of 52 = 1, 2, 4, 13, 26, 52

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The common factors of 52 and 48 are 1, 2 and 4.

Example 3:

Determine the common factors of 52 and 96.

Solution:

Factors of 52 = 1, 2, 4, 13, 26, 52

Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The common factors of 52 and 96 are 1, 2 and 4.

## Frequently Asked Questions on Factors of 52

### What are the factors of 52?

The factors of 52 are the numbers that are multiplied in pairs resulting in the original number. The factors of 52 are 1, 2, 4, 13, 26 and 52.

### What is the prime factorization of 52?

The prime factorization of 52 is 2 × 2 × 13 or 22 × 13.

### What are the positive pair factors of 52?

The positive pair factors of 52 are (1, 52), (2, 26) and (4, 13)

### Mention the negative pair factors of 52.

The negative pair factors of 52 are (-1, -52), (-2, -26) and (-4, -13)

### Can the factors of 52 be fractions?

No, the factors of 52 cannot be decimals and fractions.