120 LearnersLast updated on May 26th, 2025
Factors of 567
Factors are the numbers that divide any given number evenly without 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 567, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 567?
The numbers that divide 567 evenly are known as factors of 567.
A factor of 567 is a number that divides the number without remainder.
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, and 567.
Negative factors of 567: -1, -3, -7, -9, -21, -27, -63, -81, -189, and -567.
Prime factors of 567: 3 and 7.
Prime factorization of 567: 34 × 7.
The sum of factors of 567: 1 + 3 + 7 + 9 + 21 + 27 + 63 + 81 + 189 + 567 = 969
How to Find Factors of 567?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 567. Identifying the numbers which are multiplied to get the number 567 is the multiplication method. Step 1: Multiply 567 by 1, 567 × 1 = 567. Step 2: Check for other numbers that give 567 after multiplying 3 × 189 = 567 7 × 81 = 567 9 × 63 = 567 21 × 27 = 567 Therefore, the positive factor pairs of 567 are: (1, 567), (3, 189), (7, 81), (9, 63), (21, 27). All these factor pairs result in 567. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 567 by 1, 567 ÷ 1 = 567.
Step 2: Continue dividing 567 by the numbers until the remainder becomes 0.
567 ÷ 1 = 567
567 ÷ 3 = 189
567 ÷ 7 = 81
567 ÷ 9 = 63
567 ÷ 21 = 27
Therefore, the factors of 567 are: 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.
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 567 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
567 ÷ 3 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 567 are 3 and 7.
The prime factorization of 567 is: 34 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 567 is divided by 3 to get 189.
Step 2: Now divide 189 by 3 to get 63.
Step 3: Then divide 63 by 3 to get 21.
Step 4: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 567 is: 34 × 7.
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 567: (1, 567), (3, 189), (7, 81), (9, 63), and (21, 27).
Negative factor pairs of 567: (-1, -567), (-3, -189), (-7, -81), (-9, -63), and (-21, -27).
Common Mistakes and How to Avoid Them in Factors of 567
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 567, 1 and 567 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 567 consist of -1, -3, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 567/2.5 = 226.8, 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 567 are prime numbers.
For example, 3 and 7 are the prime factors of 567, but it has other factors like 9, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 567 as 3^4 × 7 and missing all the key factors.
Factors of 567 Examples
Problem 1
There are 9 friends and 567 apples. How will they divide it equally?
They will get 63 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of friends.
567/9 = 63
Problem 2
A field is rectangular, the length of the field is 21 meters, and the total area is 567 square meters. Find the width?
27 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
567 = 21 × width
To find the value of width, we need to shift 21 to the left side.
567/21 = width
Width = 27.
Problem 3
There are 27 bags and 567 candies. How many candies will be in each bag?
Each bag will have 21 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
567/27 = 21
Problem 4
In a class, there are 567 students, and 3 groups. How many students are there in each group?
There are 189 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
567/3 = 189
Problem 5
567 books need to be arranged in 7 shelves. How many books will go on each shelf?
Each of the shelves has 81 books.
Explanation
Divide total books with shelves.
567/7 = 81
FAQs on Factors of 567
1.What are the factors of 567?
2.Mention the prime factors of 567.
3.Is 567 a multiple of 9?
4.Mention the factor pairs of 567?
5.What is the square of 567?
Important Glossaries for Factor of 567
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, and 567.
- Prime factors: The factors which are prime numbers. For example, 3 and 7 are prime factors of 567.
- 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 567 are (1, 567), (3, 189), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For instance, the prime factorization of 567 is 34 × 7.
- Negative factors: The negative counterparts of the positive factors. For example, -1, -3, -7 are negative factors of 567.
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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.
