103 LearnersLast updated on May 26th, 2025
Factors of 2352
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 2352, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2352?
The numbers that divide 2352 evenly are known as factors of 2352.
A factor of 2352 is a number that divides the number without remainder.
The factors of 2352 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 104, 108, 117, 144, 156, 216, 234, 312, 351, 432, 468, 702, 936, 1053, 1404, 2352.
Negative factors of 2352: -1, -2, -3, -4, -6, -8, -9, -12, -13, -16, -18, -24, -26, -27, -36, -39, -52, -54, -72, -78, -104, -108, -117, -144, -156, -216, -234, -312, -351, -432, -468, -702, -936, -1053, -1404, -2352.
Prime factors of 2352: 2, 3, and 13.
Prime factorization of 2352: 2^4 × 3^2 × 13.
The sum of factors of 2352 is 8640.
How to Find Factors of 2352?
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 2352. Identifying the numbers which are multiplied to get the number 2352 is the multiplication method.
Step 1: Multiply 2352 by 1, 2352 × 1 = 2352.
Step 2: Check for other numbers that give 2352 after multiplying
2 × 1176 = 2352
3 × 784 = 2352
4 × 588 = 2352
6 × 392 = 2352
8 × 294 = 2352
9 × 261 = 2352
12 × 196 = 2352
13 × 181 = 2352
16 × 147 = 2352
18 × 130.67 ≠ 2352 (not an integer) ...
Therefore, the positive factor pairs of 2352 are: (1, 2352), (2, 1176), (3, 784), (4, 588), (6, 392), (8, 294), (9, 261), (12, 196), (13, 181), etc.
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 in whole numbers as factors. Factors can be calculated by the simple division method -
Step 1: Divide 2352 by 1, 2352 ÷ 1 = 2352.
Step 2: Continue dividing 2352 by the numbers until the remainder becomes 0.
2352 ÷ 1 = 2352
2352 ÷ 2 = 1176
2352 ÷ 3 = 784
2352 ÷ 4 = 588
2352 ÷ 6 = 392
2352 ÷ 8 = 294
2352 ÷ 9 = 261
2352 ÷ 12 = 196
2352 ÷ 13 = 181
Therefore, the factors of 2352 are: 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 104, 108, 117, 144, 156, 216, 234, 312, 351, 432, 468, 702, 936, 1053, 1404, 2352.
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 2352 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2352 ÷ 2 = 1176
1176 ÷ 2 = 588
588 ÷ 2 = 294
294 ÷ 2 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 2352 are 2, 3, and 13.
The prime factorization of 2352 is: 2^4 × 3^2 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2352 is divided by 2 to get 1176.
Step 2: Now divide 1176 by 2 to get 588.
Step 3: Then divide 588 by 2 to get 294.
Step 4: Divide 294 by 2 to get 147.
Step 5: Divide 147 by 3 to get 49.
Step 6: Divide 49 by 7 to get 7.
Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 2352 is: 2^4 × 3^2 × 13.
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 2352: (1, 2352), (2, 1176), (3, 784), (4, 588), (6, 392), (8, 294), (9, 261), (12, 196), (13, 181), etc.
Negative factor pairs of 2352: (-1, -2352), (-2, -1176), (-3, -784), (-4, -588), (-6, -392), (-8, -294), (-9, -261), (-12, -196), (-13, -181), etc.
Common Mistakes and How to Avoid Them in Factors of 2352
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 2352, 1 and 2352 are also factors.
Factors of 2352 Examples
Problem 1
A concert hall has 2352 seats and is divided into 6 sections. How many seats are in each section?
Each section has 392 seats.
Explanation
To divide the seats equally, we need to divide the total seats by the number of sections.
2352/6 = 392
Problem 2
A rectangular garden has an area of 2352 square meters and a length of 36 meters. What is the width of the garden?
The width of the garden is 65.33 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2352 = 36 × width
To find the value of the width, we need to shift 36 to the left side.
2352/36 ≈ 65.33
Problem 3
A basketball court is 13 meters wide and has an area of 2352 square meters. What is the length of the court?
The length of the court is 181 meters.
Explanation
To find the length of the court, divide the total area by the width.
2352/13 = 181
Problem 4
A library has 2352 books and 9 shelves. How many books will be on each shelf?
Each shelf will have 261 books.
Explanation
Divide the total number of books by the number of shelves to find the number of books on each shelf.
2352/9 = 261
Problem 5
A warehouse has 2352 boxes to be loaded onto 18 trucks. How many boxes will each truck carry?
Each truck will carry 130.67 boxes.
Explanation
Divide the total number of boxes by the number of trucks.
2352/18 ≈ 130.67
FAQs on Factors of 2352
1.What are the factors of 2352?
2.Mention the prime factors of 2352.
3.Is 2352 a multiple of 4?
4.Mention the factor pairs of 2352?
5.What is the square of 2352?
6.How can children in Australia use numbers in everyday life to understand Factors of 2352?
7.What are some fun ways kids in Australia can practice Factors of 2352 with numbers?
8.What role do numbers and Factors of 2352 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 2352 skills?
Important Glossaries for Factors of 2352
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2352 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 2352.
- 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 2352 are (1, 2352), (2, 1176), etc.
- Prime factorization: The method of expressing a number as the product of its prime factors. The prime factorization of 2352 is 2^4 × 3^2 × 13.
- Division method: A method of finding factors by dividing the number by integers and checking for a zero remainder. For example, factors of 2352 can be found using the division method.
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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.
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