101 LearnersLast updated on May 26th, 2025
Factors of 396
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 396, how they are used in real life, and tips to learn them quickly.
What are the Factors of 396?
The numbers that divide 396 evenly are known as factors of 396.
A factor of 396 is a number that divides the number without a remainder.
The factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, and 396.
Negative factors of 396: -1, -2, -3, -4, -6, -9, -11, -12, -18, -22, -33, -36, -44, -66, -99, -132, -198, and -396.
Prime factors of 396: 2, 3, and 11.
Prime factorization of 396: 22 × 32 × 11.
The sum of factors of 396: 1 + 2 + 3 + 4 + 6 + 9 + 11 + 12 + 18 + 22 + 33 + 36 + 44 + 66 + 99 + 132 + 198 + 396 = 1107
How to Find Factors of 396?
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 396. Identifying the numbers which are multiplied to get the number 396 is the multiplication method.
Step 1: Multiply 396 by 1, 396 × 1 = 396.
Step 2: Check for other numbers that give 396 after multiplying 2 × 198 = 396 3 × 132 = 396 4 × 99 = 396 6 × 66 = 396 9 × 44 = 396 11 × 36 = 396 12 × 33 = 396 18 × 22 = 396
Therefore, the positive factor pairs of 396 are: (1, 396), (2, 198), (3, 132), (4, 99), (6, 66), (9, 44), (11, 36), (12, 33), and (18, 22).
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 the simple division method
Step 1: Divide 396 by 1, 396 ÷ 1 = 396.
Step 2: Continue dividing 396 by the numbers until the remainder becomes 0.
396 ÷ 1 = 396
396 ÷ 2 = 198
396 ÷ 3 = 132
396 ÷ 4 = 99
396 ÷ 6 = 66
396 ÷ 9 = 44
396 ÷ 11 = 36
396 ÷ 12 = 33
396 ÷ 18 = 22
Therefore, the factors of 396 are: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 396 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
396 ÷ 2 = 198
198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 396 are 2, 3, and 11.
The prime factorization of 396 is: 22 × 32 × 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, 396 is divided by 2 to get 198.
Step 2: Now divide 198 by 2 to get 99.
Step 3: Then divide 99 by 3 to get 33.
Step 4: Divide 33 by 3 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 396 is: 22 × 32 × 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 396: (1, 396), (2, 198), (3, 132), (4, 99), (6, 66), (9, 44), (11, 36), (12, 33), and (18, 22).
Negative factor pairs of 396: (-1, -396), (-2, -198), (-3, -132), (-4, -99), (-6, -66), (-9, -44), (-11, -36), (-12, -33), and (-18, -22).
Common Mistakes and How to Avoid Them in Factors of 396
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 396, 1 and 396 are also factors.
Factors of 396 Examples
Problem 1
A concert has 396 seats, and there are 18 rows. How many seats are in each row?
Each row will have 22 seats.
Explanation
To find the number of seats in each row, divide the total seats by the number of rows.
396/18 = 22
Problem 2
A garden is rectangular, the length of the garden is 33 meters, and the total area is 396 square meters. Find the width.
12 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 396 = 33 × width
To find the value of the width, divide the area by the length.
396/33 = width
Width = 12.
Problem 3
There are 44 boxes, and each box has an equal number of apples, totaling 396 apples. How many apples are in each box?
Each box will have 9 apples.
Explanation
To find the apples in each box, divide the total apples by the number of boxes.
396/44 = 9
Problem 4
A school has 396 students and 11 buses. How many students are there in each bus?
There are 36 students in each bus.
Explanation
Dividing the students by the total number of buses will give the number of students in each bus.
396/11 = 36
Problem 5
396 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each shelf will have 66 books.
Explanation
Divide total books by the number of shelves.
396/6 = 66
FAQs on Factors of 396
1.What are the factors of 396?
2.Mention the prime factors of 396.
3.Is 396 a multiple of 9?
4.Mention the factor pairs of 396?
5.What is the square of 396?
6.How can children in Australia use numbers in everyday life to understand Factors of 396?
7.What are some fun ways kids in Australia can practice Factors of 396 with numbers?
8.What role do numbers and Factors of 396 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 396 skills?
Important Glossaries for Factor of 396
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, and 396.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 396.
- 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 396 are (1, 396), (2, 198), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 396 is 2^2 × 3^2 × 11.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 396 is a multiple of 9.
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About BrightChamps in Australia
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.
