116 LearnersLast updated on May 26th, 2025
Factors of 207
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 207, how they are used in real life, and tips to learn them quickly.
What are the Factors of 207?
The numbers that divide 207 evenly are known as factors of 207.
A factor of 207 is a number that divides the number without remainder.
The factors of 207 are 1, 3, 9, 23, 69, and 207.
Negative factors of 207: -1, -3, -9, -23, -69, and -207.
Prime factors of 207: 3 and 23.
Prime factorization of 207: 3 × 69, and 69 can be broken further to 3 × 23.
Thus, 3² × 23. The sum of factors of 207: 1 + 3 + 9 + 23 + 69 + 207 = 312
How to Find Factors of 207?
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 207. Identifying the numbers multiplied to get the number 207 is the multiplication method.
Step 1: Multiply 207 by 1, 207 × 1 = 207.
Step 2: Check for other numbers that give 207 after multiplying
3 × 69 = 207
9 × 23 = 207
Therefore, the positive factor pairs of 207 are: (1, 207), (3, 69), (9, 23).
All these factor pairs result in 207.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number by 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 207 by 1, 207 ÷ 1 = 207.
Step 2: Continue dividing 207 by the numbers until the remainder becomes 0.
207 ÷ 1 = 207
207 ÷ 3 = 69
207 ÷ 9 = 23
Therefore, the factors of 207 are: 1, 3, 9, 23, 69, 207.
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 207 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
207 ÷ 3 = 69
69 ÷ 3 = 23
23 ÷ 23 = 1
The prime factors of 207 are 3 and 23.
The prime factorization of 207 is: 3² × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 207 is divided by 3 to get 69.
Step 2: Now divide 69 by 3 to get 23.
Here, 23 is a prime number, so it cannot be divided further.
So, the prime factorization of 207 is: 3² × 23.
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 207: (1, 207), (3, 69), (9, 23).
Negative factor pairs of 207: (-1, -207), (-3, -69), (-9, -23).
Common Mistakes and How to Avoid Them in Factors of 207
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 207, 1 and 207 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 207 consist of -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 207/1.5 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 207 are prime numbers. For example, 3 and 23 are the prime factors of 207, but it has other factors like 9, 69.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 207 properly, such as missing the prime factorization 3² × 23.
Factors of 207 Examples
Problem 1
There are 9 students in a group project, and there are 207 pages to print. How many pages will each student print if divided equally?
Each student will print 23 pages.
Explanation
To divide the pages equally, we need to divide the total pages by the number of students.
207/9 = 23
Problem 2
A rectangular plot has a length of 23 meters and a total area of 207 square meters. Find the width.
9 meters.
Explanation
To find the width of the plot, we use the formula, Area = length × width
207 = 23 × width
To find the value of width, we need to rearrange the equation.
207/23 = width
Width = 9.
Problem 3
There are 3 classrooms with a total of 207 chairs. How many chairs are there in each classroom?
Each classroom has 69 chairs.
Explanation
To find the number of chairs in each classroom, divide the total chairs by the number of classrooms.
207/3 = 69
FAQs on Factors of 207
1.What are the factors of 207?
2.Mention the prime factors of 207.
3.Is 207 a multiple of 9?
4.Mention the factor pairs of 207.
5.What is the square of 207?
6.How can children in India use numbers in everyday life to understand Factors of 207?
7.What are some fun ways kids in India can practice Factors of 207 with numbers?
8.What role do numbers and Factors of 207 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 207 skills?
Important Glossaries for Factors of 207
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 207 are 1, 3, 9, 23, 69, and 207.
- Prime factors: The factors which are prime numbers. For example, 3 and 23 are prime factors of 207.
- 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 207 are (1, 207), (3, 69), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 207 is 3² × 23.
- Multiples: A multiple is a number that can be divided by another number without a remainder. For example, 207 is a multiple of 3 and 9.
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About BrightChamps in India
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.
