100 LearnersLast updated on May 26th, 2025
Factors of 1986
Factors are the numbers that divide any given number evenly without a 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 1986, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1986?
The numbers that divide 1986 evenly are known as factors of 1986.
A factor of 1986 is a number that divides the number without remainder.
The factors of 1986 are 1, 2, 3, 331, 662, and 1986.
Negative factors of 1986: -1, -2, -3, -331, -662, and -1986.
Prime factors of 1986: 2, 3, and 331.
Prime factorization of 1986: 2 × 3 × 331.
The sum of factors of 1986: 1 + 2 + 3 + 331 + 662 + 1986 = 2985
How to Find Factors of 1986?
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 1986. Identifying the numbers which are multiplied to get the number 1986 is the multiplication method.
Step 1: Multiply 1986 by 1, 1986 × 1 = 1986.
Step 2: Check for other numbers that give 1986 after multiplying
2 × 993 = 1986
3 × 662 = 1986
Therefore, the positive factor pairs of 1986 are: (1, 1986), (2, 993), (3, 662), (331, 6).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1986 by 1, 1986 ÷ 1 = 1986.
Step 2: Continue dividing 1986 by the numbers until the remainder becomes 0.
1986 ÷ 1 = 1986
1986 ÷ 2 = 993
1986 ÷ 3 = 662
1986 ÷ 331 = 6
Therefore, the factors of 1986 are: 1, 2, 3, 331, 662, 1986.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 1986 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1986 ÷ 2 = 993
993 ÷ 3 = 331
331 ÷ 331 = 1
The prime factors of 1986 are 2, 3, and 331.
The prime factorization of 1986 is: 2 × 3 × 331.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1986 is divided by 2 to get 993.
Step 2: Now divide 993 by 3 to get 331.
Step 3: 331 is a prime number, so it cannot be divided further. Thus, the prime factorization of 1986 is: 2 × 3 × 331.
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 1986: (1, 1986), (2, 993), (3, 662), (331, 6).
Negative factor pairs of 1986: (-1, -1986), (-2, -993), (-3, -662), (-331, -6).
Common Mistakes and How to Avoid Them in Factors of 1986
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 1986, 1 and 1986 are also factors.
Factors of 1986 Examples
Problem 1
There are 6 teams and 1986 apples. How will they divide them equally?
They will get 331 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of teams.
1986/6 = 331
Problem 2
A garden is rectangular, and the length of the garden is 3 meters with a total area of 1986 square meters. Find the width?
662 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1986 = 3 × width
To find the value of width, we need to shift 3 to the left side.
1986/3 = width
Width = 662.
Problem 3
There are 993 oranges and 2 boxes. How many oranges will be in each box?
Each box will have 496.5 oranges.
Explanation
To find the oranges in each box, divide the total oranges by the boxes.
993/2 = 496.5
Problem 4
In a class, there are 1986 students, and 3 groups. How many students are there in each group?
There are 662 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1986/3 = 662
Problem 5
1986 books need to be arranged in 331 shelves. How many books will go on each shelf?
Each shelf has 6 books.
Explanation
Divide total books by shelves.
1986/331 = 6
FAQs on Factors of 1986
1.What are the factors of 1986?
2.Mention the prime factors of 1986.
3.Is 1986 a multiple of 3?
4.Mention the factor pairs of 1986?
5.What is the cube of 1986?
6.How can children in Canada use numbers in everyday life to understand Factors of 1986?
7.What are some fun ways kids in Canada can practice Factors of 1986 with numbers?
8.What role do numbers and Factors of 1986 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1986 skills?
Important Glossaries for Factors of 1986
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1986 are 1, 2, 3, 331, 662, and 1986.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 331 are prime factors of 1986.
- 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 1986 are (1, 1986), (2, 993), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. The prime factorization of 1986 is 2 × 3 × 331.
- Negative factors: Factors that are negative numbers. For example, the negative factors of 1986 are -1, -2, -3, etc.
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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.
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