102 LearnersLast updated on May 26th, 2025
Factors of 837
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 837, how they are used in real life, and tips to learn them quickly.
What are the Factors of 837?
The numbers that divide 837 evenly are known as factors of 837.
A factor of 837 is a number that divides the number without a remainder.
The factors of 837 are 1, 3, 9, 27, 31, 93, 279, and 837.
Negative factors of 837: -1, -3, -9, -27, -31, -93, -279, and -837.
Prime factors of 837: 3 and 31.
Prime factorization of 837: 33 × 31.
The sum of factors of 837: 1 + 3 + 9 + 27 + 31 + 93 + 279 + 837 = 1240
How to Find Factors of 837?
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 837. Identifying the numbers which are multiplied to get the number 837 is the multiplication method.
Step 1: Multiply 837 by 1, 837 × 1 = 837.
Step 2: Check for other numbers that give 837 after multiplying
3 × 279 = 837
9 × 93 = 837
27 × 31 = 837
Therefore, the positive factor pairs of 837 are: (1, 837), (3, 279), (9, 93), and (27, 31).
All these factor pairs result in 837.
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 as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 837 by 1, 837 ÷ 1 = 837.
Step 2: Continue dividing 837 by the numbers until the remainder becomes 0.
837 ÷ 1 = 837
837 ÷ 3 = 279
837 ÷ 9 = 93
837 ÷ 27 = 31
Therefore, the factors of 837 are: 1, 3, 9, 27, 31, 93, 279, 837.
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 837 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
837 ÷ 3 = 279
279 ÷ 3 = 93
93 ÷ 3 = 31
31 ÷ 31 = 1
The prime factors of 837 are 3 and 31.
The prime factorization of 837 is: 33 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 837 is divided by 3 to get 279.
Step 2: Now divide 279 by 3 to get 93.
Step 3: Then divide 93 by 3 to get 31. Here, 31 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 837 is: 33 × 31.
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 837: (1, 837), (3, 279), (9, 93), and (27, 31).
- Negative factor pairs of 837: (-1, -837), (-3, -279), (-9, -93), and (-27, -31).
Common Mistakes and How to Avoid Them in Factors of 837
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 837, 1 and 837 are also factors.
Factors of 837 Examples
Problem 1
There are 9 teams and 837 points. How will they distribute it equally?
They will get 93 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
837/9 = 93
Problem 2
A room is rectangular, the width of the room is 27 meters, and the total area is 837 square meters. Find the length.
31 meters.
Explanation
To find the length of the room, we use the formula,
Area = length × width
837 = 27 × length
To find the value of length, we need to shift 27 to the left side.
837/27 = length
Length = 31.
Problem 3
There are 279 marbles and 3 containers. How many marbles will be in each container?
Each container will have 93 marbles.
Explanation
To find the marbles in each container, divide the total marbles by the containers.
279/3 = 93
Problem 4
In a class, there are 837 students, and 3 sections. How many students are there in each section?
There are 279 students in each section.
Explanation
Dividing the students by the total sections, we will get the number of students in each section.
837/3 = 279
Problem 5
837 apples need to be arranged in 31 baskets. How many apples will go in each basket?
Each of the baskets has 27 apples.
Explanation
Divide total apples by baskets.
837/31 = 27
FAQs on Factors of 837
1.What are the factors of 837?
2.Mention the prime factors of 837.
3.Is 837 a multiple of 9?
4.Mention the factor pairs of 837?
5.What is the square of 837?
Important Glossaries for Factors of 837
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 837 are 1, 3, 9, 27, 31, 93, 279, and 837.
- Prime factors: The factors which are prime numbers. For example, 3 and 31 are prime factors of 837.
- 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 837 are (1, 837), (3, 279), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 837 is 33 × 31.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, 9 × 93 = 837 is a factor pair.
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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.
