Factors Of 52 | How to Find Them By Prime Factorization

Factors Of 52

To get 52 as a product value, multiply 52 by the factors that are multiplied in pairs. 52 can have both positive and negative pair factors.

For instance, pair factors are (1, 52) and (-1, 52). They are multiplying -1 and -52 resulting in the original number 52 when we multiply the two negative factors together.

Using the prime factorization method with many solved examples, you will learn the factors of 52, pair factors, and prime factors of 52 and the steps on how to find the factors of 52.

What are the Factors of 52?

As you know, an original number is divided completely by its factors without leaving any remainder. So, the factors of 52 are all the numbers multiplied in pairs. In this case, the result of the multiplication is 52. There are many factors involved in the number 52 besides only one and the number itself.

Factors of 52: 1, 2, 4, 13, 26, and 52.

Prime Factorization of 52: 2 × 2 × 13

How to Find the Prime Factors of 52?

Find 52’s factors by following the steps below. Here they are:

Step 1: Write the factorization number down.

Step 2: Find two numbers with the same product as the initial number.

Let’s say that two factors, 2 and 26, are factors of 52.

Since 2 is a prime number, it can’t be factored further.

Here is an example of a composite number: 26.

Hence, 26 can be further divided into 2 and 13.

Thus, 52 is calculated by multiplying 2, 2, and 13.

As a result, you can represent 52 as 2 × 2 × 13 = 4 × 13 = 52.

Pair Factors of 52

It is called a pair factor of 52 if multiplying two numbers results in 52. There are positive and negative pair factors for 52. Here are some positive pair factors for 52.

On the other hand, the negative pair factors of 52 are:

Note:

• 52 can have negative pair factors as well.
• A factor of 52 cannot be either a decimal or a fraction.

Prime Factorization of 52

Prime factorization is a process of determining the product of the prime factors of a number. Utilizing the prime factorization method, the following steps can help you find factors of 52.

Multiply the factors of 52 to get the original number 52.

Let’s find out if 52 is a prime or composite number.

If both are prime numbers, you can directly multiply the two multipliers of 52.

Alternatively, if one of the factors of 52 is prime and the other is composite, divide and create a prime factor from the composite factor and multiply the prime factors together.

The two factors of fifty-two will be composite numbers, so you will divide these composite factors further into the prime factors, then multiply those prime factors.

By using the prime factorization method, we will find the prime factors regarding 52.

So, Take into account the pair factor of 52, (4, 13)

The number 13 is a prime factor of the pair factor (4, 13), so leave it as it is.

In the same way, consider the other factor, 4, which is composite, and you can represent it as the product of 2 and 2.

Therefore, 52 is equal to 2 × 2 × 13.

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

Examples

Example 1:

Identify the common factor of 52 and 36.

Solution:

52 has factors 1, 2, 4, 13, 26 and 52

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

In this case, 52 and 36 have the same factors 1, 2, and 4.

Example 2:

Calculate the common factor of 52 and 24.

Solution:

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

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

52 and 24 have the same factors 1, 2, and 4.

Example 3:

Calculate 52 and 45’s common factors.

Solution:

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

In this case, Factors of 45 are 1, 3, 5, 9, 15, and 45.

In 52 and 45, the common factor is 1.

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