108 LearnersLast updated on May 26th, 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
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.
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
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 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.
The prime factorization of 356 is: 2² × 89.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
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 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 356: (1, 356), (2, 178), (4, 89).
Negative factor pairs of 356: (-1, -356), (-2, -178), (-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.
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
There are 178 apples and 2 baskets. How many apples will be in each basket?
Each basket will have 89 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
178/2 = 89
Problem 4
In a class, there are 356 students, and 178 groups. How many students are there in each group?
There are 2 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
356/178 = 2
Problem 5
356 books need to be arranged in 89 shelves. How many books will go on each shelf?
Each of the shelves has 4 books.
Explanation
Divide total books by shelves.
356/89 = 4
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 can children in United States use numbers in everyday life to understand Factors of 356?
7.What are some fun ways kids in United States can practice Factors of 356 with numbers?
8.What role do numbers and Factors of 356 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 356 skills?
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.
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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.
