148 LearnersLast updated on May 26th, 2025
Factors of 657
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 657, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 657?
The numbers that divide 657 evenly are known as factors of 657. A factor of 657 is a number that divides the number without remainder. The factors of 657 are 1, 3, 9, 73, 219, and 657.
Negative factors of 657: -1, -3, -9, -73, -219, and -657.
Prime factors of 657: 3 and 73.
Prime factorization of 657: 32 × 73.
The sum of factors of 657: 1 + 3 + 9 + 73 + 219 + 657 = 962
How to Find Factors of 657?
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 657. Identifying the numbers that are multiplied to get the number 657 is the multiplication method.
Step 1: Multiply 657 by 1, 657 × 1 = 657.
Step 2: Check for other numbers that give 657 after multiplying 3 × 219 = 657 9 × 73 = 657
Therefore, the positive factor pairs of 657 are: (1, 657), (3, 219), (9, 73). All these factor pairs result in 657. 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 657 by 1, 657 ÷ 1 = 657.
Step 2: Continue dividing 657 by the numbers until the remainder becomes 0.
657 ÷ 1 = 657
657 ÷ 3 = 219
657 ÷ 9 = 73
Therefore, the factors of 657 are: 1, 3, 9, 73, 219, 657.
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 657 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
657 ÷ 3 = 219
219 ÷ 3 = 73
73 ÷ 73 = 1
The prime factors of 657 are 3 and 73. The prime factorization of 657 is: 32 × 73.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 657 is divided by 3 to get 219.
Step 2: Now divide 219 by 3 to get 73.
Step 3: 73 is a prime number and cannot be divided further. So, the prime factorization of 657 is: 32 × 73.
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 657: (1, 657), (3, 219), and (9, 73).
- Negative factor pairs of 657: (-1, -657), (-3, -219), and (-9, -73).
Common Mistakes and How to Avoid Them in Factors of 657
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 factors for every number. Always remember to include 1 and the number itself. For example, in factors of 657, 1 and 657 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 657 include -1, -3, -9, 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 657/1.5 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 657 are prime numbers. For example, 3 and 73 are the prime factors of 657, but it has other factors like 9 and 219.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors. For example, not breaking 657 as 32 × 73 and missing all the key factors.
Factors of 657 Examples
Problem 1
There are 9 classrooms and 657 students. How will they divide equally?
They will get 73 students each.
Explanation
To divide the students equally, we need to divide the total students by the number of classrooms
. 657/9 = 73
Problem 2
A rectangular garden has a length of 73 meters and the total area is 657 square meters. Find the width.
9 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
657 = 73 × width
To find the value of width, we need to shift 73 to the left side.
657/73 = width
Width = 9.
Problem 3
There are 219 candies and 3 bowls. How many candies will be in each bowl?
Each bowl will have 73 candies.
Explanation
To find the candies in each bowl, divide the total candies by the number of bowls.
219/3 = 73
Problem 4
In a hall, there are 657 chairs, and 3 rows. How many chairs are there in each row?
There are 219 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
657/3 = 219
Problem 5
657 books need to be arranged in 73 shelves. How many books will go on each shelf?
Each of the shelves has 9 books.
Explanation
Divide total books by shelves.
657/73 = 9
FAQs on Factors of 657
1.What are the factors of 657?
2.Mention the prime factors of 657.
3.Is 657 a multiple of 9?
4.Mention the factor pairs of 657.
5.What is the square of 657?
Important Glossaries for Factors of 657
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 657 are 1, 3, 9, 73, 219, and 657.
- Prime factors: The factors which are prime numbers. For example, 3 and 73 are prime factors of 657.
- 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 657 are (1, 657), (3, 219), and (9, 73).
- Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 657 is 32 × 73.
- Negative Factors: Factors of a number that are negative, such as -1, -3, -9, -73, -219, -657 for the number 657.
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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.
