100 LearnersLast updated on May 27th, 2025
Factors of 681
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 681, how they are used in real life, and tips to learn them quickly.
What are the Factors of 681?
The numbers that divide 681 evenly are known as factors of 681.
A factor of 681 is a number that divides the number without remainder.
The factors of 681 are 1, 3, 227, and 681.
Negative factors of 681: -1, -3, -227, and -681.
Prime factors of 681: 3 and 227.
Prime factorization of 681: 3 × 227.
The sum of factors of 681: 1 + 3 + 227 + 681 = 912
How to Find Factors of 681?
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 681. Identifying the numbers which are multiplied to get the number 681 is the multiplication method.
Step 1: Multiply 681 by 1, 681 × 1 = 681.
Step 2: Check for other numbers that give 681 after multiplying 3 × 227 = 681
Therefore, the positive factor pairs of 681 are: (1, 681) and (3, 227).
All these factor pairs result in 681. 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 681 by 1, 681 ÷ 1 = 681.
Step 2: Continue dividing 681 by the numbers until the remainder becomes 0.
681 ÷ 1 = 681
681 ÷ 3 = 227
Therefore, the factors of 681 are: 1, 3, 227, 681.
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 681 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
681 ÷ 3 = 227
227 ÷ 227 = 1
The prime factors of 681 are 3 and 227.
The prime factorization of 681 is: 3 × 227.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 681 is divided by 3 to get 227.
Step 2: Now divide 227 by 227 to get 1. Here, 227 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 681 is: 3 × 227.
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 681: (1, 681), (3, 227).
Negative factor pairs of 681: (-1, -681), (-3, -227).
Common Mistakes and How to Avoid Them in Factors of 681
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 681, 1 and 681 are also factors.
Factors of 681 Examples
Problem 1
There are 3 teams and 681 participants. How will they divide the participants equally?
They will have 227 participants each.
Explanation
To divide the participants equally, we need to divide the total number of participants by the number of teams.
681/3 = 227
Problem 2
A hallway is rectangular, the length of the hallway is 3 meters, and the total area is 681 square meters. Find the width?
227 meters.
Explanation
To find the width of the hallway, we use the formula, Area = length × width
681 = 3 × width
To find the value of width, we need to shift 3 to the left side.
681/3 = width
Width = 227.
Problem 3
There are 227 boxes and 681 items. How many items will be in each box?
Each box will have 3 items.
Explanation
To find the items in each box, divide the total items by the boxes.
681/227 = 3
Problem 4
In a class, there are 681 students, and 1 group. How many students are there in each group?
There are 681 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
681/1 = 681
Problem 5
681 chairs need to be arranged in 3 rows. How many chairs will go in each row?
Each of the rows has 227 chairs.
Explanation
Divide total chairs by rows.
681/3 = 227
FAQs on Factors of 681
1.What are the factors of 681?
2.Mention the prime factors of 681.
3.Is 681 a multiple of 3?
4.Mention the factor pairs of 681?
5.What is the square of 681?
6.How can children in India use numbers in everyday life to understand Factors of 681?
7.What are some fun ways kids in India can practice Factors of 681 with numbers?
8.What role do numbers and Factors of 681 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 681 skills?
Important Glossaries for Factor of 681
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 681 are 1, 3, 227, and 681.
- Prime factors: The factors which are prime numbers. For example, 3 and 227 are prime factors of 681.
- 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 681 are (1, 681) and (3, 227).
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 681 is 3 × 227.
- Multiplication method: A method to find factors by identifying pairs of 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.
