117 LearnersLast updated on May 26th, 2025
Factors of 987
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 987, how they are used in real life, and tips to learn them quickly.
What are the Factors of 987?
The numbers that divide 987 evenly are known as factors of 987.
A factor of 987 is a number that divides the number without remainder.
The factors of 987 are 1, 3, 7, 21, 47, 141, 329, and 987.
Negative factors of 987: -1, -3, -7, -21, -47, -141, -329, and -987.
Prime factors of 987: 3, 7, and 47.
Prime factorization of 987: 3 × 7 × 47.
The sum of factors of 987: 1 + 3 + 7 + 21 + 47 + 141 + 329 + 987 = 1536
How to Find Factors of 987?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 987. Identifying the numbers which are multiplied to get the number 987 is the multiplication method.
Step 1: Multiply 987 by 1, 987 × 1 = 987.
Step 2: Check for other numbers that give 987 after multiplying
3 × 329 = 987
7 × 141 = 987
21 × 47 = 987
Therefore, the positive factor pairs of 987 are: (1, 987), (3, 329), (7, 141), (21, 47).
All these factor pairs result in 987.
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 987 by 1, 987 ÷ 1 = 987.
Step 2: Continue dividing 987 by the numbers until the remainder becomes 0.
987 ÷ 1 = 987
987 ÷ 3 = 329
987 ÷ 7 = 141
987 ÷ 21 = 47
Therefore, the factors of 987 are: 1, 3, 7, 21, 47, 141, 329, 987.
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 987 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
987 ÷ 3 = 329
329 ÷ 7 = 47
47 ÷ 47 = 1
The prime factors of 987 are 3, 7, and 47.
The prime factorization of 987 is: 3 × 7 × 47.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 987 is divided by 3 to get 329.
Step 2: Now divide 329 by 7 to get 47. Step 3: 47 is a prime number and cannot be divided further. So, the prime factorization of 987 is: 3 × 7 × 47.
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 987: (1, 987), (3, 329), (7, 141), and (21, 47).
Negative factor pairs of 987: (-1, -987), (-3, -329), (-7, -141), and (-21, -47).
Common Mistakes and How to Avoid Them in Factors of 987
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 987, 1 and 987 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 987 consist of -1, -3, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 987/1.5 = 658, 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 987 are prime numbers.
For example, 3, 7, and 47 are the prime factors of 987, but it has other factors like 21, 141.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 987 as 3 × 7 × 47 and missing all the key factors.
Factors of 987 Examples
Problem 1
There are 3 friends and 987 marbles. How will they divide it equally?
They will get 329 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of friends.
987/3 = 329
Problem 2
A rectangular garden has a length of 21 meters and a total area of 987 square meters. Find the width.
47 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
987 = 21 × width
To find the value of width, we need to shift 21 to the left side.
987/21 = width
Width = 47.
Problem 3
There are 7 containers and 987 liters of water. How many liters of water will be in each container?
Each container will have 141 liters of water.
Explanation
To find the liters of water in each container, divide the total liters by the number of containers.
987/7 = 141
Problem 4
In a hall, there are 987 chairs, and 47 sections. How many chairs are there in each section?
There are 21 chairs in each section.
Explanation
Dividing the chairs by the total sections, we will get the number of chairs in each section.
987/47 = 21
Problem 5
987 students need to be divided into 3 teams. How many students will be on each team?
Each team will have 329 students.
Explanation
Divide the total students by the number of teams.
987/3 = 329
FAQs on Factors of 987
1.What are the factors of 987?
2.Mention the prime factors of 987.
3.Is 987 a multiple of 7?
4.Mention the factor pairs of 987?
5.What is the square of 987?
Important Glossaries for Factor of 987
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 987 are 1, 3, 7, 21, 47, 141, 329, and 987.
- Prime factors: The factors which are prime numbers. For example, 3, 7, and 47 are prime factors of 987.
- 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 987 are (1, 987), (3, 329), etc.
- Prime factorization: A way of expressing a number as the product of its prime factors. For example, 987 = 3 × 7 × 47.
- Multiples: A number that can be divided by another number without leaving a remainder. For example, 987 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.
