116 LearnersLast updated on May 26th, 2025
Factors of 993
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 993, how they are used in real life, and tips to learn them quickly.
What are the Factors of 993?
The numbers that divide 993 evenly are known as factors of 993.
A factor of 993 is a number that divides the number without remainder.
The factors of 993 are 1, 3, 331, and 993.
Negative factors of 993: -1, -3, -331, and -993.
Prime factors of 993: 3 and 331.
Prime factorization of 993: 3 × 331.
The sum of factors of 993: 1 + 3 + 331 + 993 = 1328
How to Find Factors of 993?
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 993. Identifying the numbers which are multiplied to get the number 993 is the multiplication method.
Step 1: Multiply 993 by 1, 993 × 1 = 993.
Step 2: Check for other numbers that give 993 after multiplying 3 × 331 = 993
Therefore, the positive factor pairs of 993 are: (1, 993) and (3, 331).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 993 by 1, 993 ÷ 1 = 993.
Step 2: Continue dividing 993 by the numbers until the remainder becomes 0.
993 ÷ 1 = 993
993 ÷ 3 = 331
Therefore, the factors of 993 are: 1, 3, 331, 993.
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 993 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
993 ÷ 3 = 331
331 ÷ 331 = 1
The prime factors of 993 are 3 and 331.
The prime factorization of 993 is: 3 × 331.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 993 is divided by 3 to get 331.
Step 2: Now divide 331 by 331 to get 1. Here, 331 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 993 is: 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 993: (1, 993) and (3, 331).
Negative factor pairs of 993: (-1, -993) and (-3, -331).
Common Mistakes and How to Avoid Them in Factors of 993
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 993, 1 and 993 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 993 consist of -1, -3, -331, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 993/1.5 = 662, 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 993 are prime numbers.
For example, 3 and 331 are the prime factors of 993, but it has other factors like 993.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 993 as 3 × 331 and missing all the key factors.
Factors of 993 Examples
Problem 1
There are 3 teams and 993 marbles. How will they divide it equally?
They will get 331 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of teams.
993/3 = 331
Problem 2
A rectangular banner's length is 3 meters, and the total area is 993 square meters. Find the width?
331 meters.
Explanation
To find the width of the banner, we use the formula,
Area = length × width
993 = 3 × width
To find the value of width, we need to shift 3 to the left side.
993/3 = width
Width = 331.
Problem 3
There are 993 candies and 1 container. How many candies will be in the container?
The container will have 993 candies.
Explanation
To find the candies in the container, divide the total candies by the number of containers.
993/1 = 993
Problem 4
In a class, there are 993 worksheets, and they need to be grouped into sets of 3. How many sets are there?
There are 331 sets.
Explanation
Dividing the worksheets by the number of sets, we will get the number of worksheets in each set.
993/3 = 331
Problem 5
993 books need to be arranged in 3 sections. How many books will go in each section?
Each of the sections has 331 books.
Explanation
Divide total books by sections.
993/3 = 331
FAQs on Factors of 993
1.What are the factors of 993?
2.Mention the prime factors of 993.
3.Is 993 a multiple of 3?
4.Mention the factor pairs of 993?
5.What is the square of 993?
Important Glossaries for Factors of 993
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 993 are 1, 3, 331, and 993.
- Prime factors: The factors which are prime numbers. For example, 3 and 331 are prime factors of 993.
- 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 993 are (1, 993) and (3, 331).
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 993 is 3 × 331.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 993 is a multiple of 3.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 993
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.
