120 LearnersLast updated on May 26th, 2025
Factors of 564
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
- Finding factors using the division method
- Prime factors and prime factorization
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.
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
- Using factor tree
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.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 564, 1 and 564 are also factors.
Mistake 2
Missing Negative Factors
We have often used only to mention positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 564 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 564/1.5 = 376, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 564 are prime numbers. 2, 3, and 47 are the prime factors of 564, but it has other factors like 4, 6, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 564 as 2² × 3 × 47 and missing all the key factors.
Factors of 564 Examples
Problem 1
There are 12 teams and 564 points. How will they distribute it equally?
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
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?
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.
Problem 3
There are 47 packages and 564 items. How many items will be in each package?
Each package will have 12 items.
Explanation
To find the items in each package, divide the total items by the packages.
564/47 = 12
Problem 4
In a competition, there are 564 participants and 3 groups. How many participants are there in each group?
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
Problem 5
564 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has 141 books.
Explanation
Divide total books with shelves.
564/4 = 141
FAQs on Factors of 564
1.What are the factors of 564?
2.Mention the prime factors of 564.
3.Is 564 a multiple of 6?
4.Mention the factor pairs of 564?
5.What is the square of 564?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 564?
7.What are some fun ways kids in Bahrain can practice Factors of 564 with numbers?
8.What role do numbers and Factors of 564 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 564 skills?
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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About BrightChamps in Bahrain
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.
