120 LearnersLast updated on May 26th, 2025
Factors of 686
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 686, how they are used in real life, and tips to learn them quickly.
What are the Factors of 686?
The numbers that divide 686 evenly are known as factors of 686.
A factor of 686 is a number that divides the number without remainder.
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, and 686.
Negative factors of 686: -1, -2, -7, -14, -49, -98, -343, and -686.
Prime factors of 686: 2 and 7.
Prime factorization of 686: 2 × 7³.
The sum of factors of 686: 1 + 2 + 7 + 14 + 49 + 98 + 343 + 686 = 1200
How to Find Factors of 686?
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 686. Identifying the numbers which are multiplied to get the number 686 is the multiplication method.
Step 1: Multiply 686 by 1, 686 × 1 = 686.
Step 2: Check for other numbers that give 686 after multiplying 2 × 343 = 686 7 × 98 = 686 14 × 49 = 686
Therefore, the positive factor pairs of 686 are: (1, 686), (2, 343), (7, 98), (14, 49).
All these factor pairs result in 686. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Divide the given number with whole numbers until the remainder becomes zero and list out the numbers which result as whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 686 by 1, 686 ÷ 1 = 686.
Step 2: Continue dividing 686 by the numbers until the remainder becomes 0.
686 ÷ 1 = 686
686 ÷ 2 = 343
686 ÷ 7 = 98
686 ÷ 14 = 49
Therefore, the factors of 686 are: 1, 2, 7, 14, 49, 98, 343, 686.
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 686 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
686 ÷ 2 = 343
343 ÷ 7 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 686 are 2 and 7.
The prime factorization of 686 is: 2 × 7³.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 686 is divided by 2 to get 343.
Step 2: Now divide 343 by 7 to get 49.
Step 3: Then divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 686 is: 2 × 7³.
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 686: (1, 686), (2, 343), (7, 98), (14, 49).
Negative factor pairs of 686: (-1, -686), (-2, -343), (-7, -98), (-14, -49).
Common Mistakes and How to Avoid Them in Factors of 686
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 686, 1 and 686 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 686 consist of -1, -2, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 3.5 is a factor because 686/3.5 ≈ 196, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 686 are prime numbers. 2 and 7 are the prime factors of 686, but it has other factors like 14, 49.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 686 as 2 × 7³ and missing all the key factors.
Factors of 686 Examples
Problem 1
There are 7 teams and 686 balls. How will they distribute them equally?
They will give 98 balls to each team.
Explanation
To divide the balls equally, we need to divide the total balls by the number of teams.
686/7 = 98
Problem 2
A hall is rectangular, the length of the hall is 14 meters and the total area is 686 square meters. Find the width.
49 meters.
Explanation
To find the width of the hall, we use the formula,
Area = length × width
686 = 14 × width
To find the value of width, we need to shift 14 to the left side.
686/14 = width
Width = 49.
Problem 3
There are 2 sections and 686 chairs. How many chairs will be in each section?
Each section will have 343 chairs.
Explanation
To find the chairs in each section, divide the total chairs by the sections.
686/2 = 343
Problem 4
In a competition, there are 686 participants, and 49 groups. How many participants are there in each group?
There are 14 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
686/49 = 14
Problem 5
686 books need to be arranged in 7 shelves. How many books will go on each shelf?
Each of the shelves has 98 books.
Explanation
Divide total books by shelves.
686/7 = 98
FAQs on Factors of 686
1.What are the factors of 686?
2.Mention the prime factors of 686.
3.Is 686 a multiple of 7?
4.Mention the factor pairs of 686.
5.What is the square of 686?
6.How can children in India use numbers in everyday life to understand Factors of 686?
7.What are some fun ways kids in India can practice Factors of 686 with numbers?
8.What role do numbers and Factors of 686 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 686 skills?
Important Glossaries for Factor of 686
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 686 are 1, 2, 7, 14, 49, 98, 343, and 686.
- Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 686.
- 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 686 are (1, 686), (2, 343), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
- Division method: A method to find factors by dividing the number by whole numbers and checking for no remainder.
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About BrightChamps in India
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.
