100 LearnersLast updated on May 26th, 2025
Factors of 2268
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 2268, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2268?
The numbers that divide 2268 evenly are known as factors of 2268.
A factor of 2268 is a number that divides the number without remainder.
The factors of 2268 include 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 567, 756, 1134, and 2268.
Negative factors of 2268: -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -42, -54, -63, -84, -108, -126, -189, -252, -378, -567, -756, -1134, -2268.
Prime factors of 2268: 2, 3, and 7.
Prime factorization of 2268: 2² × 3^4 × 7.
The sum of factors of 2268: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 42 + 54 + 63 + 84 + 108 + 126 + 189 + 252 + 378 + 567 + 756 + 1134 + 2268 = 6048
How to Find Factors of 2268?
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 2268. Identifying the numbers which are multiplied to get the number 2268 is the multiplication method.
Step 1: Multiply 2268 by 1, 2268 × 1 = 2268.
Step 2: Check for other numbers that give 2268 after multiplying:
2 × 1134 = 2268
3 × 756 = 2268
4 × 567 = 2268
6 × 378 = 2268
9 × 252 = 2268
12 × 189 = 2268
18 × 126 = 2268
27 × 84 = 2268
36 × 63 = 2268
42 × 54 = 2268
Therefore, the positive factor pairs of 2268 are: (1, 2268), (2, 1134), (3, 756), (4, 567), (6, 378), (9, 252), (12, 189), (18, 126), (27, 84), (36, 63), (42, 54).
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 in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 2268 by 1, 2268 ÷ 1 = 2268.
Step 2: Continue dividing 2268 by the numbers until the remainder becomes 0.
2268 ÷ 1 = 2268
2268 ÷ 2 = 1134
2268 ÷ 3 = 756
2268 ÷ 4 = 567
2268 ÷ 6 = 378
2268 ÷ 9 = 252
2268 ÷ 12 = 189
2268 ÷ 18 = 126
2268 ÷ 27 = 84
2268 ÷ 36 = 63
2268 ÷ 42 = 54
Therefore, the factors of 2268 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 567, 756, 1134, 2268.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 2268 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2268 ÷ 2 = 1134
1134 ÷ 2 = 567
567 ÷ 3 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 2268 are 2, 3, and 7.
The prime factorization of 2268 is: 2² × 3^4 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 2268 is divided by 2 to get 1134.
Step 2: Now divide 1134 by 2 to get 567.
Step 3: Then divide 567 by 3 to get 189.
Step 4: Divide 189 by 3 to get 63.
Step 5: Divide 63 by 3 to get 21.
Step 6: Finally, divide 21 by 3 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 2268 is: 2² × 3^4 × 7.
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 2268: (1, 2268), (2, 1134), (3, 756), (4, 567), (6, 378), (9, 252), (12, 189), (18, 126), (27, 84), (36, 63), (42, 54).
Negative factor pairs of 2268: (-1, -2268), (-2, -1134), (-3, -756), (-4, -567), (-6, -378), (-9, -252), (-12, -189), (-18, -126), (-27, -84), (-36, -63), (-42, -54).
Common Mistakes and How to Avoid Them in Factors of 2268
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 2268, 1 and 2268 are also factors.
Factors of 2268 Examples
Problem 1
There are 9 teams and 2268 players. How will they divide the players equally?
Each team will have 252 players.
Explanation
To divide the players equally, we need to divide the total players by the number of teams.
2268/9 = 252
Problem 2
A rectangular garden has a length of 12 meters and a total area of 2268 square meters. Find the width.
189 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2268 = 12 × width
To find the value of width, we need to shift 12 to the left side.
2268/12 = width
Width = 189.
Problem 3
There are 18 groups and 2268 participants. How many participants will be in each group?
Each group will have 126 participants.
Explanation
To find the participants in each group, divide the total participants by the number of groups.
2268/18 = 126
Problem 4
In a conference, there are 378 attendees and 6 rooms. How many attendees are there in each room?
There are 63 attendees in each room.
Explanation
Dividing the attendees by the total rooms, we will get the number of attendees in each room.
378/6 = 63
Problem 5
2268 books need to be arranged in 27 shelves. How many books will go on each shelf?
Each shelf will have 84 books.
Explanation
Divide total books by shelves.
2268/27 = 84
FAQs on Factors of 2268
1.What are the factors of 2268?
2.Mention the prime factors of 2268.
3.Is 2268 a multiple of 9?
4.Mention the factor pairs of 2268?
5.What is the square of 2268?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 2268?
7.What are some fun ways kids in Vietnam can practice Factors of 2268 with numbers?
8.What role do numbers and Factors of 2268 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 2268 skills?
Important Glossaries for Factors of 2268
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2268 are 1, 2, 3, 4, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 2268.
- 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 2268 are (1, 2268), (2, 1134), etc.
- Prime factorization: The expression of a number as a product of its prime numbers. For example, the prime factorization of 2268 is 2² × 3^4 × 7.
- Multiplication method: A method to find factors by identifying pairs of numbers that, when multiplied, result in the original number. For example, for 2268, (6, 378) is a factor pair through multiplication.
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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.
