100 LearnersLast updated on May 27th, 2025
Factors of 680
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 680, how they are used in real life, and tips to learn them quickly.
What are the Factors of 680?
The numbers that divide 680 evenly are known as factors of 680.
A factor of 680 is a number that divides the number without a remainder.
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, and 680.
Negative factors of 680: -1, -2, -4, -5, -8, -10, -17, -20, -34, -40, -68, -85, -136, -170, -340, and -680.
Prime factors of 680: 2, 5, and 17.
Prime factorization of 680: (23 times 5 times 17).
The sum of factors of 680: 1 + 2 + 4 + 5 + 8 + 10 + 17 + 20 + 34 + 40 + 68 + 85 + 136 + 170 + 340 + 680 = 1620
How to Find Factors of 680?
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 680. Identifying the numbers which are multiplied to get the number 680 is the multiplication method.
Step 1: Multiply 680 by 1, (680 times 1 = 680).
Step 2: Check for other numbers that give 680 after multiplying
(2 times 340 = 680)
(4 times 170 = 680)
(5 times 136 = 680)
(8 times 85 = 680)
(10 times 68 = 680)
(17 times 40 = 680)
(20 times 34 = 680)
Therefore, the positive factor pairs of 680 are: (1, 680), (2, 340), (4, 170), (5, 136), (8, 85), (10, 68), (17, 40), (20, 34). 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 680 by 1, (680 div 1 = 680).
Step 2: Continue dividing 680 by the numbers until the remainder becomes 0.
(680 div 1 = 680)
(680 div 2 = 340)
(680 div 4 = 170)
(680 div 5 = 136)
(680 div 8 = 85)
(680 div 10 = 68)
(680 div 17 = 40)
(680 div 20 = 34)
Therefore, the factors of 680 are: 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
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 680 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
(680 div 2 = 340)
(340 div 2 = 170)
(170 div 2 = 85)
(85 div 5 = 17)
(17 div 17 = 1)
The prime factors of 680 are 2, 5, and 17.
The prime factorization of 680 is: (23 times 5 times 17).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 680 is divided by 2 to get 340.
Step 2: Now divide 340 by 2 to get 170.
Step 3: Then divide 170 by 2 to get 85.
Step 4: Divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 680 is: (23 times 5 times 17).
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 680: (1, 680), (2, 340), (4, 170), (5, 136), (8, 85), (10, 68), (17, 40), (20, 34).
Negative factor pairs of 680: (-1, -680), (-2, -340), (-4, -170), (-5, -136), (-8, -85), (-10, -68), (-17, -40), (-20, -34).
Common Mistakes and How to Avoid Them in Factors of 680
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 680, 1 and 680 are also factors.
Factors of 680 Examples
Problem 1
There are 68 people and 680 apples. How will they divide them equally?
They will get 10 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
(680 div 68 = 10)
Problem 2
A rectangular garden has a length of 34 meters and a total area of 680 square meters. Find the width.
20 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
(680 = 34 times text{width})
To find the value of width, we need to shift 34 to the left side.
(680 div 34 = text{width})
Width = 20.
Problem 3
There are 136 containers and 680 liters of water. How many liters will be in each container?
Each container will have 5 liters.
Explanation
To find the volume in each container, divide the total liters by the number of containers.
(680 div 136 = 5)
Problem 4
In a workshop, there are 680 tools, and 10 sections. How many tools are there in each section?
There are 68 tools in each section.
Explanation
Dividing the tools by the total sections, we will get the number of tools in each section.
(680 div 10 = 68)
Problem 5
680 chairs need to be arranged in 17 rows. How many chairs will go in each row?
Each row has 40 chairs.
Explanation
Divide the total chairs by the number of rows.
(680 div 17 = 40)
FAQs on Factors of 680
1.What are the factors of 680?
2.Mention the prime factors of 680.
3.Is 680 a multiple of 8?
4.Mention the factor pairs of 680?
5.What is the square of 680?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 680?
7.What are some fun ways kids in United Kingdom can practice Factors of 680 with numbers?
8.What role do numbers and Factors of 680 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 680 skills?
Important Glossaries for Factors of 680
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 680 are 1, 2, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 17 are prime factors of 680.
- 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 680 are (1, 680), (2, 340), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For 680, it is (23 times 5 times 17).
- Multiplication method: A method to find factors by identifying pairs of numbers multiplied to produce the given number.
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About BrightChamps in United Kingdom
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.
