118 LearnersLast updated on May 26th, 2025
Factors of 984
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 984, how they are used in real life, and tips to learn them quickly.
What are the Factors of 984?
The numbers that divide 984 evenly are known as factors of 984.
A factor of 984 is a number that divides the number without remainder.
The factors of 984 are 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 328, 492, and 984.
Negative factors of 984: -1, -2, -3, -4, -6, -12, -41, -82, -123, -164, -246, -328, -492, and -984.
Prime factors of 984: 2, 3, and 41.
Prime factorization of 984: 2³ × 3 × 41.
The sum of factors of 984: 1 + 2 + 3 + 4 + 6 + 12 + 41 + 82 + 123 + 164 + 246 + 328 + 492 + 984 = 2488
How to Find Factors of 984?
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 984. Identifying the numbers which are multiplied to get the number 984 is the multiplication method.
Step 1: Multiply 984 by 1, 984 × 1 = 984.
Step 2: Check for other numbers that give 984 after multiplying
2 × 492 = 984
3 × 328 = 984
4 × 246 = 984
6 × 164 = 984
12 × 82 = 984
41 × 24 = 984
Therefore, the positive factor pairs of 984 are: (1, 984), (2, 492), (3, 328), (4, 246), (6, 164), (12, 82), and (41, 24).
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 984 by 1, 984 ÷ 1 = 984.
Step 2: Continue dividing 984 by the numbers until the remainder becomes 0.
984 ÷ 1 = 984
984 ÷ 2 = 492
984 ÷ 3 = 328
984 ÷ 4 = 246
984 ÷ 6 = 164
984 ÷ 12 = 82
984 ÷ 41 = 24
Therefore, the factors of 984 are: 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 328, 492, 984.
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 984 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
984 ÷ 2 = 492
492 ÷ 2 = 246
246 ÷ 2 = 123
123 ÷ 3 = 41
41 ÷ 41 = 1
The prime factors of 984 are 2, 3, and 41.
The prime factorization of 984 is: 2³ × 3 × 41.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 984 is divided by 2 to get 492.
Step 2: Now divide 492 by 2 to get 246.
Step 3: Then divide 246 by 2 to get 123.
Step 4: Divide 123 by 3 to get 41. Here, 41 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 984 is: 2³ × 3 × 41.
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 984: (1, 984), (2, 492), (3, 328), (4, 246), (6, 164), (12, 82), and (41, 24).
Negative factor pairs of 984: (-1, -984), (-2, -492), (-3, -328), (-4, -246), (-6, -164), (-12, -82), and (-41, -24).
Common Mistakes and How to Avoid Them in Factors of 984
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 as a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 984, 1 and 984 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 984 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes include fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 984/1.5 = 656, which 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 984 are prime numbers.
For example, 2, 3, and 41 are the prime factors of 984, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 984 as 2³ × 3 × 41 and missing all the key factors.
Factors of 984 Examples
Problem 1
There are 12 workers and 984 bricks. How will they distribute them equally?
They will get 82 bricks each.
Explanation
To divide the bricks equally, we need to divide the total bricks by the number of workers.
984/12 = 82
Problem 2
A rectangular garden has a length of 41 meters and a total area of 984 square meters. Find the width?
24 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
984 = 41 × width
To find the value of width, we need to shift 41 to the left side.
984/41 = width
Width = 24.
Problem 3
There are 6 boxes and 984 apples. How many apples will be in each box?
Each box will have 164 apples.
Explanation
To find the apples in each box, divide the total number of apples by the boxes.
984/6 = 164
Problem 4
In a school, there are 328 students and 4 buses. How many students are there in each bus?
There are 82 students in each bus.
Explanation
Dividing the students by the total buses, we will get the number of students in each bus.
328/4 = 82
Problem 5
984 pencils need to be arranged in 82 boxes. How many pencils will go in each box?
Each box will have 12 pencils.
Explanation
Divide total pencils by boxes.
984/82 = 12
FAQs on Factors of 984
1.What are the factors of 984?
2.Mention the prime factors of 984.
3.Is 984 a multiple of 12?
4.Mention the factor pairs of 984?
5.What is the square of 984?
Important Glossaries for Factors of 984
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 984 are 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 328, 492, and 984.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 41 are prime factors of 984.
- 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 984 are (1, 984), (2, 492), etc.
- Prime factorization: The breakdown of a number into the product of its prime factors. For example, the prime factorization of 984 is 2³ × 3 × 41.
- Multiplication method: A method to find factors by identifying all pairs of numbers that multiply to the original number. For example, using the multiplication method to find factor pairs of 984.
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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.
