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218 LearnersLast updated on December 17, 2025
Factors of 296
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 296, how they are used in real life, and tips to learn them quickly.
What are the Factors of 296?
The numbers that divide 296 evenly are known as factors of 296.
A factor of 296 is a number that divides the number without remainder.
The factors of 296 are 1, 2, 4, 8, 37, 74, 148, and 296.
Negative factors of 296: -1, -2, -4, -8, -37, -74, -148, and -296.
Prime factors of 296: 2 and 37.
Prime factorization of 296: 2³ × 37.
The sum of factors of 296: 1 + 2 + 4 + 8 + 37 + 74 + 148 + 296 = 570
| Factor Type | Values |
| Positive Factors of 296 | (1, 2, 4, 8, 37, 74, 148, 296) |
| Negative Factors of 296 | (-1, -2, -4, -8, -37, -74, -148, -296) |
| Prime Factors of 296 | (2, 37) |
| Prime Factorization of 296 | 2³ × 37 |
| Sum of factors of 296 | 570 |
How to Find Factors of 296?
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 296. Identifying the numbers which are multiplied to get the number 296 is the multiplication method.
Step 1: Multiply 296 by 1, 296 × 1 = 296.
Step 2: Check for other numbers that give 296 after multiplying
2 × 148 = 296
4 × 74 = 296
8 × 37 = 296
Therefore, the positive factor pairs of 296 are: (1, 296), (2, 148), (4, 74), (8, 37).
All these factor pairs result in 296.
For every positive factor, there is a negative factor.
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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 a simple division method -
Step 1: Divide 296 by 1, 296 ÷ 1 = 296.
Step 2: Continue dividing 296 by the numbers until the remainder becomes 0.
296 ÷ 1 = 296
296 ÷ 2 = 148
296 ÷ 4 = 74
296 ÷ 8 = 37
Therefore, the factors of 296 are: 1, 2, 4, 8, 37, 74, 148, and 296.
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 296
Divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
296 ÷ 2 = 148
148 ÷ 2 = 74
74 ÷ 2 = 37
37 ÷ 37 = 1
The prime factors of 296 are 2 and 37.
Prime Factorization of 296
Prime Factorization breaks down the prime factors of 296.
Step 1: Firstly, 296 is divided by 2 to get 148.
Step 2: Now divide 148 by 2 to get 74.
Step 3: Then divide 74 by 2 to get 37.
Here, 37 is a prime number, which cannot be divided further.
So, the prime factorization of 296 is: 2³ × 37.
Factor Tree of 296
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
Factor Pairs of 296
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 296:
| Factors | Positive Pair Factors |
| 1 × 296 = 296 | 1, 296 |
| 2 × 148 = 296 | 2, 148 |
| 4 × 74 = 296 | 4, 74 |
| 8 × 37 = 296 | 8, 37 |
Negative factor pairs of 296:
| Factors | Negative Pair Factors |
| −1 × −296 = 296 | −1, −296 |
| −2 × −148 = 296 | −2, −148 |
| −4 × −74 = 296 | −4, −74 |
| −8 × −37 = 296 | −8, −37 |
Common Mistakes and How to Avoid Them in Factors of 296
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 296, 1 and 296 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 296 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 296/1.5 = 197.333, 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 296 are prime numbers.
For example, 2 and 37 are the prime factors of 296, but it has other factors like 4, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 296 as 2³ × 37 and missing all the key factors.
Factors of 296 Examples
Problem 1
There are 8 students participating in a project, and they have 296 pages to review. How many pages will each student review equally?
Each student will review 37 pages.
Explanation
To divide the pages equally, we need to divide the total pages by the number of students.
296/8 = 37
Problem 2
A garden is rectangular, the length of the garden is 37 meters, and the total area is 296 square meters. Find the width?
8 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
296 = 37 × width
To find the value of width, we need to shift 37 to the left side.
296/37 = width
Width = 8.
Problem 3
A Walmart store in Chicago is reconciling grocery bills after correcting a sales-tax error. The accounting system shows a 296 USD adjustment that must be divided into equal whole-dollar corrections across departments. What are all the factors of 296 that represent possible equal splits?
1, 2, 4, 8, 37, 74, 148, 296
Explanation
To find the factors of 296, start with its prime factorization.
296 = 2³ × 37
All factors are formed by multiplying powers of 2 with 37 or without it.
Each resulting number divides 296 exactly with no remainder, giving the full list of factors.
Problem 4
In a Boston middle-school science lab, students analyze pharmacy inventory similar to data used by CVS pharmacies. A sample contains 296 mg of a compound that must be divided into equal integer dosage units. Which numbers are factors of 296?
1, 2, 4, 8, 37, 74, 148, 296
Explanation
A factor is a number that divides 296 evenly with no remainder.
Using the prime factorization 2³ × 37, all valid combinations produce the factors listed.
Each of these values allows the dosage to be split evenly.
Problem 5
An NCAA team in Dallas reviews travel expenses after a game in Houston. Based on gas prices per gallon, the team logs 296 gallons of fuel usage that must be divided evenly across fuel records. What are all the factors of 296 that allow an exact split?
1, 2, 4, 8, 37, 74, 148, 296
Explanation
Equal distribution requires numbers that divide 296 without leaving a remainder.
Since 296 has a limited set of divisors from its prime factors, only those values work.
These divisors represent all valid equal splits of the fuel amount.
FAQs on Factors of 296
1.What are the factors of 296?
2.Mention the prime factors of 296.
3.Is 296 a multiple of 4?
4.Mention the factor pairs of 296?
5.What is the square of 296?
6.How many factors does 296 have?
7.What is the smallest factor of 296?
8.What is the largest factor of 296?
9.Which factors of 296 add up to 13?
10.How many even factors does 296 have?
11.What are the odd factors of 296?
12.What is the sum of all the factors of 296?
Important Glossaries for Factor of 296
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 296 are 1, 2, 4, 8, 37, 74, 148, and 296.
- Prime factors: The factors which are prime numbers. For example, 2 and 37 are prime factors of 296.
- 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 296 are (1, 296), (2, 148), etc.
- Prime factorization: Breaking down a number into a product of its prime factors. For example, the prime factorization of 296 is 2³ × 37.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
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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.
