102 LearnersLast updated on May 27th, 2025
Factors of 676
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 676, how they are used in real life, and tips to learn them quickly.
What are the Factors of 676?
The numbers that divide 676 evenly are known as factors of 676.
A factor of 676 is a number that divides the number without remainder.
The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, and 676.
Negative factors of 676: -1, -2, -4, -13, -26, -52, -169, -338, and -676.
Prime factors of 676: 2 and 13.
Prime factorization of 676: 2² × 13².
The sum of factors of 676: 1 + 2 + 4 + 13 + 26 + 52 + 169 + 338 + 676 = 1281
How to Find Factors of 676?
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 676. Identifying the numbers which are multiplied to get the number 676 is the multiplication method.
Step 1: Multiply 676 by 1, 676 × 1 = 676.
Step 2: Check for other numbers that give 676 after multiplying
2 × 338 = 676
4 × 169 = 676
13 × 52 = 676
Therefore, the positive factor pairs of 676 are: (1, 676), (2, 338), (4, 169), (13, 52). All these factor pairs result in 676. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 676 by 1, 676 ÷ 1 = 676.
Step 2: Continue dividing 676 by the numbers until the remainder becomes 0.
676 ÷ 1 = 676
676 ÷ 2 = 338
676 ÷ 4 = 169
676 ÷ 13 = 52
Therefore, the factors of 676 are: 1, 2, 4, 13, 26, 52, 169, 338, 676.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 676 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
676 ÷ 2 = 338
338 ÷ 2 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1
The prime factors of 676 are 2 and 13.
The prime factorization of 676 is: 2² × 13².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 676 is divided by 2 to get 338.
Step 2: Now divide 338 by 2 to get 169.
Step 3: Then divide 169 by 13 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 676 is: 2² × 13².
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 676: (1, 676), (2, 338), (4, 169), and (13, 52).
Negative factor pairs of 676: (-1, -676), (-2, -338), (-4, -169), and (-13, -52).
Common Mistakes and How to Avoid Them in Factors of 676
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 676, 1 and 676 are also factors.
Factors of 676 Examples
Problem 1
A group of 13 friends wants to donate 676 books equally to a library. How many books will each friend donate?
Each friend will donate 52 books.
Explanation
To divide the books equally, we need to divide the total books by the number of friends.
676/13 = 52
Problem 2
A square garden has an area of 676 square meters. Find the length of one side of the garden.
26 meters.
Explanation
To find the length of one side of the garden, we use the formula, Area = side × side
676 = side × side
Taking square root on both sides, √676 = side
Side = 26.
Problem 3
A farmer has 4 plots of land, each with an equal number of trees. If there are a total of 676 trees, how many trees are in each plot?
Each plot will have 169 trees.
Explanation
To find the number of trees in each plot, divide the total trees by the number of plots.
676/4 = 169
Problem 4
There are 2 trucks, and they need to transport a total of 676 crates. How many crates will each truck carry?
Each truck will carry 338 crates.
Explanation
Dividing the crates with the total trucks, we will get the number of crates in each truck.
676/2 = 338
Problem 5
A company has 676 workstations and needs to assign them to 13 teams. How many workstations will each team get?
Each team will get 52 workstations.
Explanation
Divide total workstations by the number of teams.
676/13 = 52
FAQs on Factors of 676
1.What are the factors of 676?
2.Mention the prime factors of 676.
3.Is 676 a multiple of 13?
4.Mention the factor pairs of 676?
5.What is the square root of 676?
Important Glossaries for Factors of 676
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, and 676.
- Prime factors: The factors which are prime numbers. For example, 2 and 13 are prime factors of 676.
- 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 676 are (1, 676), (2, 338), etc.
- Square root: A number which produces a specified quantity when multiplied by itself. For example, the square root of 676 is 26.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 676 is 2² × 13².
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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.
