100 LearnersLast updated on May 27th, 2025
Factors of 682
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 682, how they are used in real life, and tips to learn them quickly.
What are the Factors of 682?
The numbers that divide 682 evenly are known as factors of 682.
A factor of 682 is a number that divides the number without a remainder.
The factors of 682 are 1, 2, 11, 22, 31, 62, 341, and 682.
Negative factors of 682: -1, -2, -11, -22, -31, -62, -341, and -682.
Prime factors of 682: 2, 11, and 31.
Prime factorization of 682: 2 × 11 × 31.
The sum of factors of 682: 1 + 2 + 11 + 22 + 31 + 62 + 341 + 682 = 1152
How to Find Factors of 682?
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 682. Identifying the numbers which are multiplied to get the number 682 is the multiplication method.
Step 1: Multiply 682 by 1, 682 × 1 = 682.
Step 2: Check for other numbers that give 682 after multiplying
2 × 341 = 682
11 × 62 = 68
22 × 31 = 682
Therefore, the positive factor pairs of 682 are: (1, 682), (2, 341), (11, 62), (22, 31). All these factor pairs result in 682.
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 the simple division method
Step 1: Divide 682 by 1, 682 ÷ 1 = 682.
Step 2: Continue dividing 682 by the numbers until the remainder becomes 0.
682 ÷ 1 = 682
682 ÷ 2 = 341
682 ÷ 11 = 62
682 ÷ 22 = 31
Therefore, the factors of 682 are: 1, 2, 11, 22, 31, 62, 341, 682.
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 682 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
682 ÷ 2 = 341
341 ÷ 11 = 31
31 ÷ 31 = 1
The prime factors of 682 are 2, 11, and 31.
The prime factorization of 682 is: 2 × 11 × 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, 682 is divided by 2 to get 341.
Step 2: Now divide 341 by 11 to get 31. Here, 31 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 682 is: 2 × 11 × 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 682: (1, 682), (2, 341), (11, 62), (22, 31).
Negative factor pairs of 682: (-1, -682), (-2, -341), (-11, -62), (-22, -31).
Common Mistakes and How to Avoid Them in Factors of 682
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 682, 1 and 682 are also factors.
Factors of 682 Examples
Problem 1
There are 31 birds and 682 seeds. How will they divide it equally?
They will get 22 seeds each.
Explanation
To divide the seeds equally, we need to divide the total seeds with the number of birds.
682 / 31 = 22
Problem 2
A rectangular garden has a length of 31 meters and a total area of 682 square meters. Find the width?
22 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
682 = 31 × width
To find the value of width, we need to shift 31 to the left side.
682 / 31 = width
Width = 22.
Problem 3
There are 11 cartons and 682 apples. How many apples will be in each carton?
Each carton will have 62 apples.
Explanation
To find the apples in each carton, divide the total apples by the number of cartons.
682 / 11 = 62
Problem 4
A library has 682 books and 2 shelves. How many books are there on each shelf?
There are 341 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
682 / 2 = 341
Problem 5
682 pages need to be printed in 341 books. How many pages will each book have?
Each book will have 2 pages.
Explanation
Divide the total pages by the number of books.
682 / 341 = 2
FAQs on Factors of 682
1.What are the factors of 682?
2.Mention the prime factors of 682.
3.Is 682 a multiple of 11?
4.Mention the factor pairs of 682?
5.What is the square of 682?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 682?
7.What are some fun ways kids in United Kingdom can practice Factors of 682 with numbers?
8.What role do numbers and Factors of 682 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 682 skills?
Important Glossaries for Factor of 682
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 682 are 1, 2, 11, 22, 31, 62, 341, and 682.
- Prime factors: The factors which are prime numbers. For example, 2, 11, and 31 are prime factors of 682.
- 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 682 are (1, 682), (2, 341), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For instance, the prime factorization of 682 is 2 × 11 × 31.
- Negative factors: Factors that are negative. For example, the negative factors of 682 are -1, -2, -11, -22, -31, -62, -341, and -682.
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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.
