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276 LearnersLast updated on December 17, 2025
Factors of 356
Factors are the numbers that divide any given number evenly without a 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 356, how they are used in real life, and tips to learn them quickly.
What are the Factors of 356?
The numbers that divide 356 evenly are known as factors of 356.
A factor of 356 is a number that divides the number without a remainder.
The factors of 356 are 1, 2, 4, 89, 178, and 356.
Negative factors of 356: -1, -2, -4, -89, -178, and -356.
Prime factors of 356: 2 and 89.
Prime factorization of 356: 2² × 89.
The sum of factors of 356: 1 + 2 + 4 + 89 + 178 + 356 = 630
| Factor Type | Values |
| Positive Factors of 356 | (1, 2, 4, 89, 178, 356) |
| Negative Factors of 356 | (-1, -2, -4, -89, -178, -356) |
| Prime Factors of 356 | (2, 89) |
| Prime Factorization of 356 | 2² × 89 |
| Sum of factors of 356 | 630 |
How to Find Factors of 356?
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 356. Identifying the numbers which are multiplied to get the number 356 is the multiplication method.
Step 1: Multiply 356 by 1, 356 × 1 = 356.
Step 2: Check for other numbers that give 356 after multiplying 2 × 178 = 356 4 × 89 = 356
Therefore, the positive factor pairs of 356 are: (1, 356), (2, 178), and (4, 89).
All these factor pairs result in 356.
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 356 by 1, 356 ÷ 1 = 356.
Step 2: Continue dividing 356 by the numbers until the remainder becomes 0.
356 ÷ 1 = 356
356 ÷ 2 = 178
356 ÷ 4 = 89
Therefore, the factors of 356 are: 1, 2, 4, 89, 178, 356.
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.
Factor Pairs of 356
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 356:
| Factors | Positive Pair Factors |
| 1 × 356 = 356 | 1, 356 |
| 2 × 178 = 356 | 2, 178 |
| 4 × 89 = 356 | 4, 89 |
Negative factor pairs of 356:
| Factors | Negative Pair Factors |
| −1 × −356 = 356 | −1, −356 |
| −2 × −178 = 356 | −2, −178 |
| −4 × −89 = 356 | −4, −89 |
Common Mistakes and How to Avoid Them in Factors of 356
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
People might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 356, 1 and 356 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 356 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Sometimes fractions are mistakenly considered as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 356/1.5 = 237.333, 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 356 are prime numbers.
For example, 2 and 89 are the prime factors of 356, but it has other factors like 4, 178.
Mistake 5
Mistake in Factorization
Skipping steps in factorization can lead to incorrect factors.
For example, not breaking 356 as 2² × 89 and missing all the key factors.
Factors of 356 Examples
Problem 1
There are 4 boxes and 356 chocolates. How will they divide it equally?
They will get 89 chocolates each.
Explanation
To divide the chocolates equally, we need to divide the total chocolates by the number of boxes.
356/4 = 89
Problem 2
A rectangular garden has a length of 89 meters and a total area of 356 square meters. Find the width.
4 meters.
Explanation
To find the width of the garden, we use the formula:
Area = length × width
356 = 89 × width
To find the value of the width, shift 89 to the left side.
356/89 = width Width = 4.
Problem 3
A Target store in Los Angeles (LA) is reconciling grocery bills and state sales tax after a system update. The final adjustment shows 356 USD that must be split into equal whole-dollar corrections across departments. What are all the factors of 356 that represent possible equal splits?
1, 2, 4, 89, 178, 356
Explanation
To find the factors of 356, start with its prime factorization.
356 = 2² × 89
All factors are formed by multiplying different combinations of these primes.
Each number listed divides 356 exactly with no remainder, so they are all valid factors.
Problem 4
In a Boston middle-school science lab, students review pharmacy inventory data similar to that used by CVS pharmacies. A sample contains 356 mg of a compound that must be divided into equal integer dosage units for testing. Which numbers are factors of 356?
1, 2, 4, 89, 178, 356
Explanation
A factor is a number that divides 356 evenly without leaving a remainder.
Using the prime factorization 2² × 89, all possible products give the complete factor list.
Each value allows the dosage to be split evenly.
Problem 5
An NHL team in Dallas reviews travel expenses after a game in Houston. Based on gas prices per gallon, the team logs 356 gallons of fuel usage that must be divided evenly across fuel records. What are all the factors of 356 that allow an exact split?
1, 2, 4, 89, 178, 356
Explanation
Equal distribution requires numbers that divide 356 with no remainder.
Since 356 = 2² × 89, it has a limited set of divisors.
Those divisors represent all the valid ways to split the fuel amount evenly.
FAQs on Factors of 356
1.What are the factors of 356?
2.Mention the prime factors of 356.
3.Is 356 a multiple of 4?
4.Mention the factor pairs of 356?
5.What is the square of 356?
6.How many factors does 356 have?
7.What is the smallest factor of 356?
8.What is the largest factor of 356?
9.Which factors of 356 add up to 13?
10.How many even factors does 356 have?
11.What are the odd factors of 356?
12.What is the sum of all the factors of 356?
Important Glossaries for Factors of 356
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 356 are 1, 2, 4, 89, 178, and 356.
- Prime factors: Factors which are prime numbers. For example, 2 and 89 are prime factors of 356.
- 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 356 are (1, 356), (2, 178), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 356 is 2² × 89.
- Multiplication method: A method to find factor pairs by identifying numbers that multiply to give the original number.
Prime factors of 356
Prime factors of 356 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
356 ÷ 2 = 178
178 ÷ 2 = 89
89 is a prime number, so it cannot be divided further.
The prime factors of 356 are 2 and 89.
Prime factorization of 356
Step 1: Firstly, 356 is divided by 2 to get 178.
Step 2: Now divide 178 by 2 to get 89.
Step 3: 89 is a prime number and cannot be divided anymore. So, the prime factorization of 356 is: 2² × 89.
Factor Tree of 356
The factor tree is the graphical representation of breaking down any number into prime factors.
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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.
