Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 7 teams and 686 balls. How will they distribute them equally?
They will give 98 balls to each team.
To divide the balls equally, we need to divide the total balls by the number of teams.
686/7 = 98
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.
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.
There are 2 sections and 686 chairs. How many chairs will be in each section?
Each section will have 343 chairs.
To find the chairs in each section, divide the total chairs by the sections.
686/2 = 343
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.
Dividing the participants by the total groups, we will get the number of participants in each group.
686/49 = 14
686 books need to be arranged in 7 shelves. How many books will go on each shelf?
Each of the shelves has 98 books.
Divide total books by shelves.
686/7 = 98
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.
: She loves to read number jokes and games.