Factors of 564
2026-02-28 11:23 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 564, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 564?

The numbers that divide 564 evenly are known as factors of 564.

A factor of 564 is a number that divides the number without a remainder.

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, and 564.

Negative factors of 564: -1, -2, -3, -4, -6, -12, -47, -94, -141, -188, -282, and -564.

Prime factors of 564: 2, 3, and 47.

Prime factorization of 564: 2² × 3 × 47.

The sum of factors of 564: 1 + 2 + 3 + 4 + 6 + 12 + 47 + 94 + 141 + 188 + 282 + 564 = 1344

How to Find Factors of 564?

Factors can be found using different methods. Mentioned below are some commonly used methods:

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 564. Identifying the numbers which are multiplied to get the number 564 is the multiplication method.

Step 1: Multiply 564 by 1, 564 × 1 = 564.

Step 2: Check for other numbers that give 564 after multiplying

2 × 282 = 564

3 × 188 = 564

4 × 141 = 564

6 × 94 = 564

12 × 47 = 564

Therefore, the positive factor pairs of 564 are: (1, 564), (2, 282), (3, 188), (4, 141), (6, 94), (12, 47). For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method -

Step 1: Divide 564 by 1, 564 ÷ 1 = 564.

Step 2: Continue dividing 564 by the numbers until the remainder becomes 0.

564 ÷ 1 = 564

564 ÷ 2 = 282

564 ÷ 3 = 188

564 ÷ 4 = 141

564 ÷ 6 = 94

564 ÷ 12 = 47

Therefore, the factors of 564 are: 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.

Prime Factors and Prime Factorization

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of 564 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.

564 ÷ 2 = 282

282 ÷ 2 = 141

141 ÷ 3 = 47

47 ÷ 47 = 1

The prime factors of 564 are 2, 3, and 47.

The prime factorization of 564 is: 2² × 3 × 47.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 564 is divided by 2 to get 282.

Step 2: Now divide 282 by 2 to get 141.

Step 3: Then divide 141 by 3 to get 47. Here, 47 is a prime number and cannot be divided anymore. So, the prime factorization of 564 is: 2² × 3 × 47.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of 564: (1, 564), (2, 282), (3, 188), (4, 141), (6, 94), (12, 47).

Negative factor pairs of 564: (-1, -564), (-2, -282), (-3, -188), (-4, -141), (-6, -94), (-12, -47).

Common Mistakes and How to Avoid Them in Factors of 564

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 12 teams and 564 points. How will they distribute it equally?

Okay, lets begin

Each team will receive 47 points.

Explanation

To distribute the points equally, we need to divide the total points by the number of teams.

564/12 = 47

Well explained 👍

Problem 2

A garden is rectangular, the length of the garden is 6 meters and the total area is 564 square meters. Find the width?

Okay, lets begin

94 meters.

Explanation

To find the width of the garden, we use the formula,

Area = length × width

564 = 6 × width

To find the value of width, we need to shift 6 to the left side.

564/6 = width

Width = 94.

Well explained 👍

Problem 3

There are 47 packages and 564 items. How many items will be in each package?

Okay, lets begin

Each package will have 12 items.

Explanation

To find the items in each package, divide the total items by the packages.

564/47 = 12

Well explained 👍

Problem 4

In a competition, there are 564 participants and 3 groups. How many participants are there in each group?

Okay, lets begin

There are 188 participants in each group.

Explanation

Dividing the participants by the total groups, we will get the number of participants in each group.

564/3 = 188

Well explained 👍

Problem 5

564 books need to be arranged in 4 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 141 books.

Explanation

Divide total books with shelves.

564/4 = 141

Well explained 👍

FAQs on Factors of 564

1.What are the factors of 564?

1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564 are the factors of 564.

2.Mention the prime factors of 564.

The prime factors of 564 are 2² × 3 × 47.

3.Is 564 a multiple of 6?

4.Mention the factor pairs of 564?

(1, 564), (2, 282), (3, 188), (4, 141), (6, 94), (12, 47) are the factor pairs of 564.

5.What is the square of 564?

Important Glossaries for Factors of 564

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, and 564.
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 47 are prime factors of 564.
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 564 are (1, 564), (2, 282), etc.
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 564 is 2² × 3 × 47.
  • Multiple: A number is a multiple of another if it can be divided by that number without a remainder. For example, 564 is a multiple of 6.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.