101 LearnersLast updated on May 26th, 2025
Factors of 1686
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 1686, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1686?
The numbers that divide 1686 evenly are known as factors of 1686.
A factor of 1686 is a number that divides the number without remainder.
The factors of 1686 are 1, 2, 3, 6, 9, 18, 31, 62, 93, 186, 281, 562, 843, and 1686.
Negative factors of 1686: -1, -2, -3, -6, -9, -18, -31, -62, -93, -186, -281, -562, -843, and -1686.
Prime factors of 1686: 2, 3, and 281.
Prime factorization of 1686: 2 × 3 × 281.
The sum of factors of 1686: 1 + 2 + 3 + 6 + 9 + 18 + 31 + 62 + 93 + 186 + 281 + 562 + 843 + 1686 = 3783
How to Find Factors of 1686?
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 1686. Identifying the numbers which are multiplied to get the number 1686 is the multiplication method.
Step 1: Multiply 1686 by 1, 1686 × 1 = 1686.
Step 2: Check for other numbers that give 1686 after multiplying
2 × 843 = 1686
3 × 562 = 1686
6 × 281 = 1686
9 × 187 = 1686
Therefore, the positive factor pairs of 1686 are: (1, 1686), (2, 843), (3, 562), (6, 281), and (9, 187).
All these factor pairs result in 1686.
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 results as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1686 by 1, 1686 ÷ 1 = 1686.
Step 2: Continue dividing 1686 by the numbers until the remainder becomes 0.
1686 ÷ 1 = 1686
1686 ÷ 2 = 843
1686 ÷ 3 = 562
1686 ÷ 6 = 281
1686 ÷ 9 = 187
Therefore, the factors of 1686 are: 1, 2, 3, 6, 9, 18, 31, 62, 93, 186, 281, 562, 843, and 1686.
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 1686 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1686 ÷ 2 = 843
843 ÷ 3 = 281
281 ÷ 281 = 1
The prime factors of 1686 are 2, 3, and 281.
The prime factorization of 1686 is: 2 × 3 × 281.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1686 is divided by 2 to get 843.
Step 2: Now divide 843 by 3 to get 281.
Step 3: Here, 281 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1686 is: 2 × 3 × 281.
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 1686: (1, 1686), (2, 843), (3, 562), (6, 281), and (9, 187).
Negative factor pairs of 1686: (-1, -1686), (-2, -843), (-3, -562), (-6, -281), and (-9, -187).
Common Mistakes and How to Avoid Them in Factors of 1686
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 1686, 1 and 1686 is also a factor.
Factors of 1686 Examples
Problem 1
There are 6 friends and 1686 pages of a book. How will they divide it equally?
They will get 281 pages each.
Explanation
To divide the pages equally, we need to divide the total pages with the number of friends.
1686/6 = 281
Problem 2
A rectangular garden has a length of 9 meters and a total area of 1686 square meters. Find the width.
187 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1686 = 9 × width
To find the value of width, we need to shift 9 to the left side.
1686/9 = width
Width = 187.
Problem 3
There are 3 classrooms and 1686 desks. How many desks will be in each classroom?
Each classroom will have 562 desks.
Explanation
To find the desks in each classroom, divide the total desks with the classrooms.
1686/3 = 562
Problem 4
In a class, there are 1686 students, and 281 groups. How many students are there in each group?
There are 6 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1686/281 = 6
Problem 5
1686 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 843 books.
Explanation
Divide total books with shelves.
1686/2 = 843
FAQs on Factors of 1686
1.What are the factors of 1686?
2.Mention the prime factors of 1686.
3.Is 1686 a multiple of 3?
4.Mention the factor pairs of 1686?
5.What is the square of 1686?
Important Glossaries for Factor of 1686
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1686 are 1, 2, 3, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 281 are prime factors of 1686.
- 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 1686 are (1, 1686), (2, 843), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For instance, 1686 = 2 × 3 × 281.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1686 is a multiple of 3.
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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.
