127 LearnersLast updated on May 26th, 2025
Factors of 357
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 357, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 357?
The numbers that divide 357 evenly are known as factors of 357.
A factor of 357 is a number that divides the number without remainder.
The factors of 357 are 1, 3, 7, 17, 21, 51, 119, and 357.
Negative factors of 357: -1, -3, -7, -17, -21, -51, -119, and -357.
Prime factors of 357: 3 and 17.
Prime factorization of 357: 3 × 7 × 17.
The sum of factors of 357: 1 + 3 + 7 + 17 + 21 + 51 + 119 + 357 = 576
How to Find Factors of 357?
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 357. Identifying the numbers which are multiplied to get the number 357 is the multiplication method.
Step 1: Multiply 357 by 1, 357 × 1 = 357.
Step 2: Check for other numbers that give 357 after multiplying 3 × 119 = 357 7 × 51 = 357 17 × 21 = 357
Therefore, the positive factor pairs of 357 are: (1, 357), (3, 119), (7, 51), (17, 21).
All these factor pairs result in 357.
For every positive factor, there is a negative factor.
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 357 by 1, 357 ÷ 1 = 357.
Step 2: Continue dividing 357 by the numbers until the remainder becomes 0.
357 ÷ 1 = 357
357 ÷ 3 = 119
357 ÷ 7 = 51
357 ÷ 17 = 21
Therefore, the factors of 357 are: 1, 3, 7, 17, 21, 51, 119, 357.
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 357 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
357 ÷ 3 = 119
119 ÷ 7 = 17
17 ÷ 17 = 1
The prime factors of 357 are 3, 7, and 17.
The prime factorization of 357 is: 3 × 7 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 357 is divided by 3 to get 119.
Step 2: Now divide 119 by 7 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 357 is: 3 × 7 × 17.
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 357: (1, 357), (3, 119), (7, 51), and (17, 21).
Negative factor pairs of 357: (-1, -357), (-3, -119), (-7, -51), and (-17, -21).
Common Mistakes and How to Avoid Them in Factors of 357
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 357, 1 and 357 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 357 consist of -1, -3, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 357/1.5 = 238, 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 357 are prime numbers.
For example, 3 and 17 are the prime factors of 357, but it has other factors like 7, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 357 as 3 × 7 × 17 and missing all the key factors.
Factors of 357 Examples
Problem 1
A group of 3 friends wants to divide 357 marbles among themselves equally. How many marbles will each friend get?
Each friend will get 119 marbles.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
357/3 = 119
Problem 2
A rectangular garden has a length of 17 meters and an area of 357 square meters. Find the width of the garden.
21 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
357 = 17 × width
To find the value of width, we need to shift 17 to the left side.
357/17 = width
Width = 21.
Problem 3
There are 357 candies and 7 jars. How many candies will be in each jar?
Each jar will have 51 candies.
Explanation
To find the candies in each jar, divide the total candies by the number of jars.
357/7 = 51
Problem 4
In a class, there are 357 students, and they want to form groups of 21. How many students will be there in each group?
17 students in each group.
Explanation
Dividing the students by the number of groups, we will get the number of students in each group.
357/21 = 17
Problem 5
357 books need to be arranged in 17 shelves. How many books will go on each shelf?
Each of the shelves will have 21 books.
Explanation
Divide total books by the number of shelves.
357/17 = 21
FAQs on Factors of 357
1.What are the factors of 357?
2.Mention the prime factors of 357.
3.Is 357 a multiple of 7?
4.Mention the factor pairs of 357?
5.What is the square of 357?
6.How can children in Singapore use numbers in everyday life to understand Factors of 357?
7.What are some fun ways kids in Singapore can practice Factors of 357 with numbers?
8.What role do numbers and Factors of 357 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve Factors of 357 skills?
Important Glossaries for Factors of 357
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 357 are 1, 3, 7, 17, 21, 51, 119, and 357.
- Prime factors: The factors which are prime numbers. For example, 3, 7, and 17 are prime factors of 357.
- 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 357 are (1, 357), (3, 119), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 357 is 3 × 7 × 17.
- Negative factors: The negative counterparts of the factors of a number. For example, the negative factors of 357 are -1, -3, -7, -17, -21, -51, -119, -357.
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About BrightChamps in Singapore
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.
