119 LearnersLast updated on May 26th, 2025
Factors of -33
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 -33, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -33?
The numbers that divide -33 evenly are known as factors of -33.
A factor of -33 is a number that divides the number without a remainder.
The factors of -33 are 1, 3, 11, and 33.
Negative factors of -33: -1, -3, -11, and -33.
Prime factors of 33: 3 and 11.
Prime factorization of 33: 3 × 11.
The sum of positive factors of 33: 1 + 3 + 11 + 33 = 48
How to Find Factors of -33?
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 33 (ignoring the sign for multiplication). Identifying the numbers which are multiplied to get the number 33 is the multiplication method.
Step 1: Multiply 33 by 1, 33 × 1 = 33.
Step 2: Check for other numbers that give 33 after multiplying 3 × 11 = 33
Therefore, the positive factor pairs of 33 are: (1, 33), (3, 11).
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 33 by 1, 33 ÷ 1 = 33.
Step 2: Continue dividing 33 by the numbers until the remainder becomes 0.
33 ÷ 1 = 33
33 ÷ 3 = 11
33 ÷ 11 = 3
Therefore, the factors of 33 are: 1, 3, 11, 33.
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 33 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 33 are 3 and 11.
The prime factorization of 33 is: 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, 33 is divided by 3 to get 11.
Step 2: Now divide 11 by 11 to get 1. Here, 11 is a prime number that cannot be divided anymore.
So, the prime factorization of 33 is: 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 33: (1, 33), (3, 11).
Negative factor pairs of 33: (-1, -33), (-3, -11).
Common Mistakes and How to Avoid Them in Factors of -33
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 33, 1 and 33 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of -33 consist of -1, -3, -11, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 33/1.5 ≈ 22, 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 33 are prime numbers. For example, 3 and 11 are the prime factors of 33, but it has other factors like 1, 33.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 33 as 3 × 11 and missing all the key factors.
Factors of -33 Examples
Problem 1
There are 3 teams and -33 points. How will they divide it equally?
They will get -11 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
-33/3 = -11
Problem 2
A rectangular garden has a length of 11 meters and a negative area of -33 square meters. What is the width?
-3 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
-33 = 11 × width
To find the value of width, we need to shift 11 to the left side.
-33/11 = width
Width = -3.
Problem 3
There are 11 groups and -33 apples. How many apples will be in each group?
Each group will have -3 apples.
Explanation
To find the apples in each group, divide the total apples by the number of groups.
-33/11 = -3
Problem 4
In a class, there are -33 students, and 3 groups. How many students are there in each group?
There are -11 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
-33/3 = -11
Problem 5
-33 books need to be arranged in 11 shelves. How many books will go on each shelf?
Each of the shelves has -3 books.
Explanation
Divide total books by shelves.
-33/11 = -3
FAQs on Factors of -33
1.What are the factors of -33?
2.Mention the prime factors of 33.
3.Is 33 a multiple of 3?
4.Mention the factor pairs of 33?
5.What is the absolute value of -33?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of -33?
7.What are some fun ways kids in United Kingdom can practice Factors of -33 with numbers?
8.What role do numbers and Factors of -33 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of -33 skills?
Important Glossaries for Factors of -33
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -33 are 1, 3, 11, 33, and their negatives.
- Prime factors: The factors which are prime numbers. For example, 3 and 11 are prime factors of 33.
- 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 33 are (1, 33), (3, 11).
- Negative factors: The factors that are negative counterparts of the positive factors. For example, -1, -3, -11, -33 are negative factors of -33.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 33 is 3 × 11.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of -33
About BrightChamps in United Kingdom
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.
