Factors

# Factors of 52 | Prime Factorization of 52 | Factor Tree of 52

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### Factors of 52 | Prime Factorization of 52 | Factor Tree of 52

**Factors of 52:** The factors of a number are a set of integers that divide the number evenly. They leave no remainder after the division.

**52 has 6 factors in total. Factors of 52 are 1, 2, 4, 13, 26 and 52**

The factors of all numbers are positive and negative. They can also occur in pairs. So, multiplying the numbers with their pairs can give a product that equals 52.

In this article, we will cover in detail the factors of 52 and how to find them using the division method, prime factorization, and factor tree method. Keep reading to learn more

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## What Are the Factors of 52?

The factors of 52 are a list of integers that divide 52 evenly. They can occur in pairs, they are also both positive and negative.

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

Negative Factors of 52: -1, -2, -4, -13, -26 and -52 |

Prime Factorization of 52: 2 X 2 X 13 or 2^{2} X 13 |

Pair Factors of 52: (1, 52); (4, 13) and (2, 26) |

Prime Factors of 52: 2 and 13 |

Sum of Factors of 52: 98 |

Sum of Prime Factors of 52: 15 |

The pair factors of a number are a set of pairs, which when multiplied by each other yield the given number as the product. These pair factors of 52 can also be written in positive or negative integers.

### Positive Pair Factors of 52

**Positive pair factors of 52: (1, 52), (2, 26), and (4, 13).**

### Negative Pair Factors of 52

**Negative pair factors of 52: (-1, -52), (-2, -26), and (-4, -13).**

## How To Find Factors of 52 Through Division Method?

We will first employ the division method to find the factors of 52. According to this approach, we will multiply a sequence of numbers by 52.

The numbers that divide 52 without leaving any reminders are its factors. The steps below present a detailed idea about how to find the factors of 52 using the division method:

• 52 ÷ 1 = 52

• 52 ÷ 2 = 26

• 52 ÷ 4 = 13

• 52 ÷ 13 = 4

• 52 ÷ 26 = 2

• 52 ÷ 52 = 1

So, we can determine that 1, 2, 4, 13, 26, and 52 are the numbers that do not leave any remainder when divided by 52. So, they are factors of 52.

## What Is the Prime Factorization of 52?

To use the prime factorization method, we must first determine if the given number is prime or composite. If the number is a prime number, it has only two factors: 1 and 52. If not, it has more than two factors.

We know that 52 is a composite number. Thus, it has over two factors. So, we can use the prime factorization method to find the factors of 52.

The steps to find prime factors of 52 using the prime factorization method are given below:

**Step 1:** Divide the number 52 by the smallest prime number that can divide evenly. That number is 2.

52 ÷ 2 = 26

**Step 2:** We get 26 as the quotient. Now, divide 26 by the smallest prime number which is 2.

26 ÷ 2 = 13

Step 3: The next quotient we got is 13. Dividing 13 with 13 gives us 1.

13 ÷ 13 = 1

The final quotient is 1. Since it cannot be divided further, the prime factors of 52 are 2 X 2 X 13 or 2^{2} X 13. We can also write it down as 2 and 13, as both of them are prime numbers.

Image representation of the prime factorization of 52:

## What is the Factor Tree of 52?

We can also use the factor tree to find the prime factors of 52. As per this method, will place 52 on top of the factor tree. We will branch it out as a set of its pair factors. These factors will be further branched out. This process will continue until all the branches have prime numbers.

**Step 1: **Let’s place the number 52 on top. Now let us choose one of its pair factors. They are 2 and 26.

**Step 2:** 2 is a prime number and we can no longer separate it. We will now divide 26 into 2 and 13.

**Step 3:** We can see that 2 and 13 are both prime numbers. All the branches in the factor tree will now be prime numbers.

Hence, circling all the branches, 2^{2} X 13 or 2 X 2 X 13= 52, which are 52 prime factors.

There are many ways in which we can write the factor tree of 52. Below is an image representation of the factor tree of 52, choosing 2 and 26 as pair factors of 52.

## Solved Examples of Factors of 52

Here are some solved examples of 52 factors:

**What is the sum of all the factors of 52?**1, 2, 4, 13, 26, and 52 are the 48 factors.

1 + 2 + 4 + 13 + 26 + 52 = 98

Hence, 98 is the sum of all 52 factors.

**What are the factors and prime factors of 52?**The factors of 52: 1, 2, 4, 13, 26, and 52.

The prime factors of 52: 13 X 2

^{2}or 2 X 2 X 13.

**What’s the highest common factor between 52 and 65?**The factors of 52 are 1, 2, 4, 13, 26, and 52.

Factors of 65 are 1, 5, 13, and 65.

Hence, from the above, the common factors of 52 and 65 are 1 and 13.

The highest common factor between 52 and 65 is 13.

**What’s the highest common factor between 52 and 32?**The factors of 52 are 1, 2, 4, 13, 26, and 52.

Factors of 32 are 1, 2, 4, 8, 16, and 32.

Hence, from the above, the common factors of 52 and 32 are 1, 2, and 4.

The highest common factor between 52 and 32 is 4.

**Is 13 a factor of 52?**Yes, 13 is a factor of 52.

As 52 ÷ 4 = 13.

**What are the factors of -52?**The factors of -52 are -1, -2, -4, -13, -26, and -52.

**What are the common factors of 48 and 52?**To find the common factors of 48 and 52, we need to find the factors of both numbers.

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

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

Hence the common factors of 52 and 54 are 1, 2, and 4.

**What are all the factors of 52?**The factors of 52 are 1, 2, 4, 13, 26, and 52.

**What are the factors of 52 that are composite?**Any number which has more than 2 factors is known as a composite number.

The list of number which has more than 2 factors in factors of 52 is 4, 26, and 52.

**What factors of 52 are multiples of 2?**The factors of 52 that are multiples of 2 are 2, 4, 26, and 52.

2 x 1 = 2

2 x 2 = 4

2 x 13 = 26

2 x 26 = 52.

**How many factors of 52 are odd?**A total of 2 odd numbers are there in factors of 52 and they are 1 and 13.

**What are the factors of 52 and 91?**The factors of 52 are 1, 2, 4, 13, 26, and 52.

The factors of 91 are 1, 7, 13, and 91.

**What are the common factors of 52 and 56?**To list out the common factors of 52 and 56, we need to find the factors of both 52 and 56.

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

Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56

From the above, the common factors of 52 and 56 are 1, 2, and 4.

**How many different factors are there for the number 52?**A total of 6 factors are there for the number 52 and they are 1, 2, 4, 13, 26, and 52.

**What factors of 52 are multiples of 4?**The factors of 52 that are multiples of 4 are 4 and 52.

**How many pair factors are there in 52?**A total of 3 pairs are there in factors of 52.

**What is the largest factor of 52?**The largest factor of 52 is 52.

The second largest factor of 52 is 26.

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## FAQs on Factors of 52

**List all the factors of 52**1, 2, 4, 13, 26, and 52 are the 52 factors.

**What are the negative factors of 52?**-1, -2, -4, -13, -26, and -52 are the 48 composite factors.

Composite factors are those that have more than 2 factors other than 1 and itself.

**What are the factors of 52 in pairs?**(1, 52), (2, 26) and (4, 13) are the 52 factors of pairs.

**What are the positive factors of 52?**1, 2, 4, 13, 26, and 52 are the positive factors for 52.

**What are the first 10 multiples of 52?**Multiples are the numbers we get when we multiply a number (52) with an integer.

The first 10 multiples of 52: 52, 104, 156, 208, 260, 312, 364, 416, 468, and 520.

We have now covered all the necessary aspects of the factors 52. We hope that this article was informational and easy to understand.

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Written by by

Prerit Jain