114 LearnersLast updated on May 26th, 2025
Factors of -132
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 -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 a remainder.
The positive 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 the positive 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 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 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 positive factors of 132 are: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. For every positive factor, there is a negative factor.
Prime Factors and Prime Factorization
The factors can be found by dividing them with a prime number. 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 and 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), (11, 12).
Negative factor pairs of -132: (-1, -132), (-2, -66), (-3, -44), (-4, -33), (-6, -22), (-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.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -132 include -1, -2, -3, 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 -132/1.5 = -88, 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 132 are prime numbers. For example, 2, 3, and 11 are the prime factors of 132, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 132 as 2² × 3 × 11 and missing all the key factors.
Factors of -132 Examples
Problem 1
There are 11 teams and 132 points. How will the points be distributed equally among the teams?
Each team will get 12 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams. 132/11 = 12
Problem 2
A rope is 132 meters long and needs to be cut into 4 equal pieces. What will be the length of each piece?
33 meters.
Explanation
To find the length of each piece, divide the total length by the number of pieces.
132/4 = 33
Problem 3
There are 66 chairs and 6 rows. How many chairs will be in each row?
Each row will have 11 chairs.
Explanation
To find the chairs in each row, divide the total chairs by the number of rows. 66/6 = 11
Problem 4
A garden has an area of 132 square meters and a width of 11 meters. What is the length of the garden?
12 meters.
Explanation
To find the length of the garden, use the formula, Area = length × width
132 = length × 11
To find the value of length, divide by 11.
132/11 = length
Length = 12.
Problem 5
132 apples need to be packed in boxes, with each box containing 22 apples. How many boxes are needed?
6 boxes.
Explanation
Divide the total apples by the number of apples per box.
132/22 = 6
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 3?
4.Mention the factor pairs of -132?
5.What is the square of 132?
Important Glossaries for Factors of -132
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -132 include ±1, ±2, ±3, etc.
- 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.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, etc., are negative factors of -132.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 132 is 2² × 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.
