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229 LearnersLast updated on December 17, 2025
Factors of 1152
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 1152, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1152?
The numbers that divide 1152 evenly are known as factors of 1152. A factor of 1152 is a number that divides the number without remainder.
The factors of 1152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, and 1152.
Negative factors of 1152: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -128, -144, -192, -288, -384, -576, and -1152.
Prime factors of 1152: 2 and 3.
Prime factorization of 1152: 27 × 32.
The sum of factors of 1152: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 64 + 72 + 96 + 128 + 144 + 192 + 288 + 384 + 576 + 1152 = 3367
| Factor Type | Values |
| Positive Factors of 36 | (1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152) |
| Negative Factors of 36 | ( -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -128, -144, -192, -288, -384, -576, -1152) |
| Prime Factors of 36 | (2, 3) |
| Prime Factorization of 36 | 27 × 32 |
| Sum of factors of 36 | 3367 |
How to Find Factors of 1152?
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 1152. Identifying the numbers which are multiplied to get the number 1152 is the multiplication method.
Step 1: Multiply 1152 by 1, 1152 × 1 = 1152.
Step 2: Check for other numbers that give 1152 after multiplying
2 × 576 = 1152
3 × 384 = 1152
4 × 288 = 1152
6 × 192 = 1152
8 × 144 = 1152
9 × 128 = 1152
12 × 96 = 1152
16 × 72 = 1152
18 × 64 = 1152
24 × 48 = 1152
32 × 36 = 1152
Therefore, the positive factor pairs of 1152 are: (1, 1152), (2, 576), (3, 384), (4, 288), (6, 192), (8, 144), (9, 128), (12, 96), (16, 72), (18, 64), (24, 48), (32, 36). For every positive factor, there is a negative factor.
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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 1152 by 1, 1152 ÷ 1 = 1152.
Step 2: Continue dividing 1152 by the numbers until the remainder becomes 0.
1152 ÷ 1 = 1152
1152 ÷ 2 = 576
1152 ÷ 3 = 384
1152 ÷ 4 = 288
1152 ÷ 6 = 192
1152 ÷ 8 = 144
1152 ÷ 9 = 128
1152 ÷ 12 = 96
1152 ÷ 16 = 72
1152 ÷ 18 = 64
1152 ÷ 24 = 48
1152 ÷ 32 = 36
Therefore, the factors of 1152 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, and 1152.
Prime Factors and Prime Factorization
- Multiplying prime numbers to get the given number as their product is called prime factors.
- Prime factorization is the process of breaking down the number into its prime factors.
Prime factors of 1152
Divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
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 1152 are 2 and 3.
Prime Factorization of 1152
Prime Factorization breaks down the prime factors of 1152.
Step 1: Firstly, 1152 is divided by 2 to get 576.
Step 2: Now divide 576 by 2 to get 288.
Step 3: Then divide 288 by 2 to get 144.
Step 4: Divide 144 by 2 to get 72.
Step 5: Divide 72 by 2 to get 36. Step 6: Divide 36 by 2 to get 18.
Step 7: Divide 18 by 2 to get 9.
Step 8: Divide 9 by 3 to get 3.
Step 9: Divide 3 by 3 to get 1. Here, 3 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1152 is: 27 × 32.
Factor Tree of 1152
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
Factor Pairs of 1152
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 1152:
| Factors | Positive Pair Factors |
| 1 × 1152 = 1152 | 1, 1152 |
| 2 × 576 = 1152 | 2, 576 |
| 3 × 384 = 1152 | 3, 384 |
| 4 × 288 = 1152 | 4, 288 |
| 6 × 192 = 1152 | 6, 192 |
| 8 × 144 = 1152 | 8, 144 |
| 9 × 128 = 1152 | 9, 128 |
| 12 × 96 = 1152 | 12, 96 |
| 16 × 72 = 1152 | 16, 72 |
| 18 × 64 = 1152 | 18, 64 |
| 24 × 48 = 1152 | 24, 48 |
| 32 × 36 = 1152 | 32, 36 |
Negative factor pairs of 1152:
| Factors | Negative Pair Factors |
| −1 × −1152 = 1152 | −1, −1152 |
| −2 × −576 = 1152 | −2, −576 |
| −3 × −384 = 1152 | −3, −384 |
| −4 × −288 = 1152 | −4, −288 |
| −6 × −192 = 1152 | −6, −192 |
| −8 × −144 = 1152 | −8, −144 |
| −9 × −128 = 1152 | −9, −128 |
| −12 × −96 = 1152 | −12, −96 |
| −16 × −72 = 1152 | −16, −72 |
| −18 × −64 = 1152 | −18, −64 |
| −24 × −48 = 1152 | −24, −48 |
| −32 × −36 = 1152 | −32, −36 |
Common Mistakes and How to Avoid Them in Factors of 1152
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 word. Always remember to include 1 and the number itself. For example, in factors of 1152, 1 and 1152 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors. For example, the factors of 1152 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor. For example, thinking 1.5 as a factor, because 1152/1.5 = 768, 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 1152 are prime numbers. For example, 2 and 3 are the prime factors of 1152, but it has other factors like 4, 6, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors. For example, not breaking 1152 as 27 × 32 and missing all the key factors.
Factors of 1152 Examples
Problem 1
There are 24 students and 1152 pencils. How will they divide it equally?
They will get 48 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of students.
1152/24 = 48
Problem 2
A garden is rectangular, the length of the garden is 12 meters and the total area is 1152 square meters. Find the width?
96 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1152 = 12 × width
To find the value of width, we need to shift 12 to the left side.
1152/12 = width
Width = 96.
Problem 3
A Costco warehouse in New York City is closing monthly grocery and sales-tax records. The system shows a $1,152 adjustment that must be split into equal whole-dollar corrections across departments. What are all the factors of 1152 that represent possible equal splits?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152
Explanation
To find the factors of 1152, first write its prime factorization.
1152 = 2โท × 3²
All factors are formed by multiplying powers of 2 (from 2โฐ to 2โท) with powers of 3 (from 3โฐ to 3²).
Each resulting number divides 1152 exactly with no remainder, giving the complete factor list.
Problem 4
In a Boston school science lab, students study medicine inventory systems used by CVS pharmacies. A compound sample contains 1,152 mg of material that must be divided into equal integer dosage units for testing. Which numbers are factors of 1152?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152
Explanation
A factor divides 1152 evenly without leaving a remainder.
Using the prime factorization 2โท × 3², all valid combinations of these primes generate the full set of divisors.
Each listed value allows the dosage to be split evenly.
Problem 5
An NFL team in Dallas reviews travel expenses after a game in Houston. Based on gas prices per gallon, the team logs 1,152 gallons of fuel usage that must be divided evenly across fuel records. What are all the factors of 1152 that allow an exact split?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152
Explanation
Equal distribution requires integers that divide 1152 with no remainder.
Because 1152 has many divisors formed from its prime factors, there are multiple valid ways to split the total evenly.
All such divisors are factors of 1152.
FAQs on Factors of 1152
1.What are the factors of 1152?
2.Mention the prime factors of 1152.
3.Is 1152 a multiple of 8?
4.Mention the factor pairs of 1152?
5.What is the cube root of 1152?
6.How many factors does 1152 have?
7.What is the smallest factor of 1152?
8.What is the largest factor of 1152?
9.Which factors of 1152 add up to 13?
10.How many even factors does 1152 have?
11.What are the odd factors of 1152?
12.What is the sum of all the factors of 1152?
Important Glossaries for Factors of 1152
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1152 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 1152.
- 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 1152 are (1, 1152), (2, 576), etc.
- Prime factorization: The expression of a number as a product of its prime numbers. For example, the prime factorization of 1152 is 27 × 32.
- Sum of factors: The total sum when all factors of a number are added together. For example, the sum of factors of 1152 is 3367.
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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.
