121 LearnersLast updated on May 26th, 2025
Factors of 999
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 999, how they are used in real life, and tips to learn them quickly.
What are the Factors of 999?
The numbers that divide 999 evenly are known as factors of 999.
A factor of 999 is a number that divides the number without remainder.
The factors of 999 are 1, 3, 9, 27, 37, 111, 333, and 999.
Negative factors of 999: -1, -3, -9, -27, -37, -111, -333, and -999.
Prime factors of 999: 3 and 37.
Prime factorization of 999: (33 × 37).
The sum of factors of 999: 1 + 3 + 9 + 27 + 37 + 111 + 333 + 999 = 1520
How to Find Factors of 999?
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 999. Identifying the numbers which are multiplied to get the number 999 is the multiplication method.
Step 1: Multiply 999 by 1, 999 × 1 = 999.
Step 2: Check for other numbers that give 999 after multiplying
3 × 333 = 999
9 × 111 = 999
27 × 37 = 999
Therefore, the positive factor pairs of 999 are: (1, 999), (3, 333), (9, 111), (27, 37).
All these factor pairs result in 999.
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 999 by 1, 999 ÷ 1 = 999.
Step 2: Continue dividing 999 by the numbers until the remainder becomes 0.
999 ÷ 1 = 999
999 ÷ 3 = 333
999 ÷ 9 = 111
999 ÷ 27 = 37
Therefore, the factors of 999 are: 1, 3, 9, 27, 37, 111, 333, 999.
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 999 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
999 ÷ 3 = 333
333 ÷ 3 = 111
111 ÷ 3 = 37
37 ÷ 37 = 1
The prime factors of 999 are 3 and 37.
The prime factorization of 999 is: \(3^3 \times 37\).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 999 is divided by 3 to get 333.
Step 2: Now divide 333 by 3 to get 111.
Step 3: Then divide 111 by 3 to get 37. Here, 37 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 999 is: (33 × 37).
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 999: (1, 999), (3, 333), (9, 111), (27, 37).
Negative factor pairs of 999: (-1, -999), (-3, -333), (-9, -111), (-27, -37).
Common Mistakes and How to Avoid Them in Factors of 999
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 999, 1 and 999 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 999 consist of -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 999/1.5 = 666, 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 999 are prime numbers.
For example, 3 and 37 are the prime factors of 999, but it has other factors like 9, 111.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 999 as (33 × 37) and missing all the key factors.
Factors of 999 Examples
Problem 1
There are 27 friends and 999 candies. How will they divide it equally?
They will get 37 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
999/27 = 37
Problem 2
A field is rectangular, the length of the field is 37 meters and the total area is 999 square meters. Find the width?
27 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
999 = 37 × width
To find the value of width, we need to shift 37 to the left side.
999/37 = width
Width = 27.
Problem 3
There are 9 bags and 999 candies. How many candies will be in each bag?
Each bag will have 111 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
999/9 = 111
Problem 4
In a class, there are 333 students, and 3 groups. How many students are there in each group?
There are 111 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
333/3 = 111
Problem 5
999 books need to be arranged in 37 shelves. How many books will go on each shelf?
Each of the shelves has 27 books.
Explanation
Divide total books with shelves.
999/37 = 27
FAQs on Factors of 999
1.What are the factors of 999?
2.Mention the prime factors of 999.
3.Is 999 a multiple of 9?
4.Mention the factor pairs of 999?
5.What is the square of 999?
6.How can children in Canada use numbers in everyday life to understand Factors of 999?
7.What are some fun ways kids in Canada can practice Factors of 999 with numbers?
8.What role do numbers and Factors of 999 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 999 skills?
Important Glossaries for Factor of 999
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 999 are 1, 3, 9, 27, 37, 111, 333, and 999.
- Prime factors: The factors which are prime numbers. For example, 3 and 37 are prime factors of 999.
- 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 999 are (1, 999), (3, 333), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 999 is (33 × 37).
- Negative factors: Factors that are negative numbers. For example, -1, -3, -9, etc., are negative factors of 999.
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About BrightChamps in Canada
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.
