102 LearnersLast updated on May 26th, 2025
Factors of 297
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 297, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 297?
The numbers that divide 297 evenly are known as factors of 297.
A factor of 297 is a number that divides the number without a remainder.
The factors of 297 are 1, 3, 9, 11, 27, 33, 99, and 297.
Negative factors of 297: -1, -3, -9, -11, -27, -33, -99, and -297.
Prime factors of 297: 3 and 11.
Prime factorization of 297: 33 × 11.
The sum of factors of 297: 1 + 3 + 9 + 11 + 27 + 33 + 99 + 297 = 480
How to Find Factors of 297?
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 297. Identifying the numbers which are multiplied to get the number 297 is the multiplication method.
Step 1: Multiply 297 by 1, 297 × 1 = 297.
Step 2: Check for other numbers that give 297 after multiplying
3 × 99 = 297
9 × 33 = 297
11 × 27 = 297
Therefore, the positive factor pairs of 297 are: (1, 297), (3, 99), (9, 33), (11, 27).
All these factor pairs result in 297.
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 as whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 297 by 1, 297 ÷ 1 = 297.
Step 2: Continue dividing 297 by the numbers until the remainder becomes 0.
297 ÷ 1 = 297
297 ÷ 3 = 99
297 ÷ 9 = 33
297 ÷ 11 = 27
Therefore, the factors of 297 are: 1, 3, 9, 11, 27, 33, 99, 297.
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 297 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
297 ÷ 3 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 297 are 3 and 11.
The prime factorization of 297 is: 33 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 297 is divided by 3 to get 99.
Step 2: Now divide 99 by 3 to get 33.
Step 3: Then divide 33 by 3 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 297 is: 33 × 11.
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 297: (1, 297), (3, 99), (9, 33), (11, 27).
Negative factor pairs of 297: (-1, -297), (-3, -99), (-9, -33), (-11, -27).
Common Mistakes and How to Avoid Them in Factors of 297
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 word. Always remember to include 1 and the number itself.
For example, in factors of 297, 1 and 297 is also a factor.
Factors of 297 Examples
Problem 1
A group of students collected 297 seashells, and they want to share them equally among 9 students. How many seashells will each student get?
Each student will get 33 seashells.
Explanation
To divide the seashells equally, we need to divide the total seashells with the number of students.
297/9 = 33
Problem 2
A garden is rectangular, the length of the garden is 27 meters and the total area is 297 square meters. Find the width?
11 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
297 = 27 × width
To find the value of width, we need to shift 27 to the left side.
297/27 = width
Width = 11.
Problem 3
There are 11 baskets and 297 apples. How many apples will be in each basket?
Each basket will have 27 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
297/11 = 27
Problem 4
A class has 297 students, divided into groups of 3. How many groups are there?
There are 99 groups.
Explanation
Dividing the students with the group size, we will get the number of groups.
297/3 = 99
Problem 5
297 books need to be arranged in 33 shelves. How many books will go on each shelf?
Each shelf will have 9 books.
Explanation
Divide total books with shelves.
297/33 = 9
FAQs on Factors of 297
1.What are the factors of 297?
2.Mention the prime factors of 297.
3.Is 297 a multiple of 9?
4.Mention the factor pairs of 297?
5.What is the square of 297?
6.How can children in Canada use numbers in everyday life to understand Factors of 297?
7.What are some fun ways kids in Canada can practice Factors of 297 with numbers?
8.What role do numbers and Factors of 297 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 297 skills?
Important Glossaries for Factor of 297
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 297 are 1, 3, 9, 11, 27, 33, 99, and 297.
- Prime factors: The factors which are prime numbers. For example, 3 and 11 are prime factors of 297.
- 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 297 are (1, 297), (3, 99), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 297 is 3^3 × 11.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 297 is a multiple of 3.
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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.
