106 LearnersLast updated on May 26th, 2025
Factors of 132
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 132, how they are used in real life, and tips to learn them quickly.
What are the Factors of 132?
The numbers that divide 132 evenly are known as factors of 132. A factor of 132 is a number that divides the number without remainder. The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.
Negative factors of 132: -1, -2, -3, -4, -6, -11, -12, -22, -33, -44, -66, and -132.
Prime factors of 132: 2, 3, and 11.
Prime factorization of 132: 22 × 3 × 11.
The sum of factors of 132: 1 + 2 + 3 + 4 + 6 + 11 + 12 + 22 + 33 + 44 + 66 + 132 = 336
How to Find Factors of 132?
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 132. Identifying the numbers which are multiplied to get the number 132 is the multiplication method.
Step 1: Multiply 132 by 1, 132 × 1 = 132.
Step 2: Check for other numbers that give 132 after multiplying 2 × 66 = 132
3 × 44 = 132
4 × 33 = 132
6 × 22 = 132
11 × 12 = 132
Therefore, the positive factor pairs of 132 are: (1, 132), (2, 66), (3, 44), (4, 33), (6, 22), (11, 12). 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 simple division method -
Step 1: Divide 132 by 1, 132 ÷ 1 = 132.
Step 2: Continue dividing 132 by the numbers until the remainder becomes 0.
132 ÷ 1 = 132
132 ÷ 2 = 66
132 ÷ 3 = 44
132 ÷ 4 = 33
132 ÷ 6 = 22
132 ÷ 11 = 12
Therefore, the factors of 132 are: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132.
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 132 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
132 ÷ 2 = 66
66 ÷ 2 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 132 are 2, 3, and 11. The prime factorization of 132 is: 22 × 3 × 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, 132 is divided by 2 to get 66.
Step 2: Now divide 66 by 2 to get 33.
Step 3: Then divide 33 by 3 to get 11. Here, 11 is a prime number, that cannot be divided anymore. So, the prime factorization of 132 is: 22 × 3 × 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 132: (1, 132), (2, 66), (3, 44), (4, 33), (6, 22), and (11, 12).
- Negative factor pairs of 132: (-1, -132), (-2, -66), (-3, -44), (-4, -33), (-6, -22), and (-11, -12).
Common Mistakes and How to Avoid Them in Factors of 132
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 132, 1 and 132 are also factors.
Factors of 132 Examples
Problem 1
A team of 12 people needs to split 132 apples equally. How many apples will each person get?
Each person will get 11 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
132/12 = 11
Problem 2
A room is 11 meters long and has an area of 132 square meters. What is the width of the room?
12 meters.
Explanation
To find the width of the room, we use the formula, Area = length × width
132 = 11 × width
To find the value of width, we need to shift 11 to the left side.
132/11 = width
Width = 12.
Problem 3
There are 6 tables and 132 chairs. How many chairs will be at each table?
Each table will have 22 chairs.
Explanation
To find the chairs at each table, divide the total chairs by the tables.
132/6 = 22
Problem 4
In a library, there are 132 books, and 11 shelves. How many books are there on each shelf?
There are 12 books on each shelf.
Explanation
Dividing the books by the total shelves, we get the number of books on each shelf.
132/11 = 12
Problem 5
A baker has 132 cupcakes and needs to arrange them in 4 boxes. How many cupcakes will go in each box?
Each box will have 33 cupcakes.
Explanation
Divide total cupcakes by boxes.
132/4 = 33
FAQs on Factors of 132
1.What are the factors of 132?
2.Mention the prime factors of 132.
3.Is 132 a multiple of 6?
4.Mention the factor pairs of 132?
5.What is the square of 132?
Important Glossaries for Factor of 132
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 132.
- 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 132 are (1, 132), (2, 66), etc.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the given number.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 132 is 2^2 × 3 × 11.
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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.
