100 LearnersLast updated on May 26th, 2025
Factors of 2304
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 2304, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2304?
The numbers that divide 2304 evenly are known as factors of 2304.
A factor of 2304 is a number that divides the number without remainder.
The factors of 2304 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152, and 2304.
Negative factors of 2304: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -128, -144, -192, -288, -384, -576, -1152, and -2304.
Prime factors of 2304: 2 and 3.
Prime factorization of 2304: 2^8 × 3^2.
The sum of factors of 2304: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 64 + 72 + 96 + 128 + 144 + 192 + 288 + 384 + 576 + 1152 + 2304 = 6552
How to Find Factors of 2304?
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 2304. Identifying the numbers that are multiplied to get the number 2304 is the multiplication method.
Step 1: Multiply 2304 by 1, 2304 × 1 = 2304.
Step 2: Check for other numbers that give 2304 after multiplying
2 × 1152 = 2304
3 × 768 = 2304
4 × 576 = 2304
6 × 384 = 2304
8 × 288 = 2304
9 × 256 = 2304
12 × 192 = 2304
16 × 144 = 2304
18 × 128 = 2304
24 × 96 = 2304
32 × 72 = 2304
36 × 64 = 2304
48 × 48 = 2304
Therefore, the positive factor pairs of 2304 are: (1, 2304), (2, 1152), (3, 768), (4, 576), (6, 384), (8, 288), (9, 256), (12, 192), (16, 144), (18, 128), (24, 96), (32, 72), (36, 64), (48, 48).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 2304 by 1, 2304 ÷ 1 = 2304.
Step 2: Continue dividing 2304 by the numbers until the remainder becomes 0.
2304 ÷ 1 = 2304
2304 ÷ 2 = 1152
2304 ÷ 3 = 768
2304 ÷ 4 = 576
2304 ÷ 6 = 384
2304 ÷ 8 = 288
2304 ÷ 9 = 256
2304 ÷ 12 = 192
2304 ÷ 16 = 144
2304 ÷ 18 = 128
2304 ÷ 24 = 96
2304 ÷ 32 = 72
2304 ÷ 36 = 64
2304 ÷ 48 = 48
Therefore, the factors of 2304 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152, 2304.
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 2304 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2304 ÷ 2 = 1152
1152 ÷ 2 = 576
576 ÷ 2 = 288
288 ÷ 2 = 144
144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 2304 are 2 and 3.
The prime factorization of 2304 is: 2^8 × 3^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2304 is divided by 2 to get 1152.
Step 2: Now divide 1152 by 2 to get 576.
Step 3: Then divide 576 by 2 to get 288.
Step 4: Divide 288 by 2 to get 144.
Step 5: Divide 144 by 2 to get 72.
Step 6: Divide 72 by 2 to get 36.
Step 7: Divide 36 by 2 to get 18.
Step 8: Divide 18 by 2 to get 9.
Step 9: Divide 9 by 3 to get 3.
Here, 3 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 2304 is: 2^8 × 3^2.
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 2304: (1, 2304), (2, 1152), (3, 768), (4, 576), (6, 384), (8, 288), (9, 256), (12, 192), (16, 144), (18, 128), (24, 96), (32, 72), (36, 64), (48, 48).
Negative factor pairs of 2304: (-1, -2304), (-2, -1152), (-3, -768), (-4, -576), (-6, -384), (-8, -288), (-9, -256), (-12, -192), (-16, -144), (-18, -128), (-24, -96), (-32, -72), (-36, -64), (-48, -48).
Common Mistakes and How to Avoid Them in Factors of 2304
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 2304, 1 and 2304 are also factors.
Factors of 2304 Examples
Problem 1
There are 24 friends and 2304 candies. How will they divide them equally?
They will get 96 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
2304 ÷ 24 = 96
Problem 2
A rectangular plot has a length of 48 meters and a total area of 2304 square meters. Find the width.
48 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
2304 = 48 × width
To find the value of width, we need to shift 48 to the left side.
2304 ÷ 48 = width
Width = 48.
Problem 3
There are 36 bags and 2304 marbles. How many marbles will be in each bag?
Each bag will have 64 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the bags.
2304 ÷ 36 = 64
Problem 4
In a class, there are 64 students, and 9 groups. How many students are there in each group?
There are 7 students in each group, with 1 student remaining.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
64 ÷ 9 = 7 (remainder 1)
Problem 5
2304 books need to be arranged in 12 shelves. How many books will go on each shelf?
Each of the shelves has 192 books.
Explanation
Divide the total books by shelves.
2304 ÷ 12 = 192
FAQs on Factors of 2304
1.What are the factors of 2304?
2.Mention the prime factors of 2304.
3.Is 2304 a multiple of 6?
4.Mention the factor pairs of 2304?
5.What is the square root of 2304?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 2304?
7.What are some fun ways kids in Vietnam can practice Factors of 2304 with numbers?
8.What role do numbers and Factors of 2304 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 2304 skills?
Important Glossaries for Factors of 2304
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2304 are 1, 2, 3, 4, 6, 8, 9, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 2304.
- 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 2304 are (1, 2304), (2, 1152), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 2304 is 2^8 × 3^2.
- Square root: A value that, when multiplied by itself, gives the original number. For example, the square root of 2304 is 48.
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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
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