118 LearnersLast updated on May 26th, 2025
Factors of 990
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 990, how they are used in real life, and tips to learn them quickly.
What are the Factors of 990?
The numbers that divide 990 evenly are known as factors of 990.
A factor of 990 is a number that divides the number without a remainder.
The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, and 990.
Negative factors of 990: -1, -2, -3, -5, -6, -9, -10, -11, -15, -18, -22, -30, -33, -45, -55, -66, -90, -99, -110, -165, -198, -330, -495, and -990.
Prime factors of 990: 2, 3, 5, and 11.
Prime factorization of 990: 2 × 32 × 5 × 11.
The sum of factors of 990: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 11 + 15 + 18 + 22 + 30 + 33 + 45 + 55 + 66 + 90 + 99 + 110 + 165 + 198 + 330 + 495 + 990 = 2970
How to Find Factors of 990?
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 990. Identifying the numbers which are multiplied to get the number 990 is the multiplication method.
Step 1: Multiply 990 by 1, 990 × 1 = 990.
Step 2: Check for other numbers that give 990 after multiplying
2 × 495 = 990
3 × 330 = 990
5 × 198 = 990
6 × 165 = 990
9 × 110 = 990
10 × 99 = 990
11 × 90 = 990
15 × 66 = 990
18 × 55 = 990
22 × 45 = 990
30 × 33 = 990
Therefore, the positive factor pairs of 990 are: (1, 990), (2, 495), (3, 330), (5, 198), (6, 165), (9, 110), (10, 99), (11, 90), (15, 66), (18, 55), (22, 45), and (30, 33).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 990 by 1, 990 ÷ 1 = 990.
Step 2: Continue dividing 990 by the numbers until the remainder becomes 0.
990 ÷ 1 = 990
990 ÷ 2 = 495
990 ÷ 3 = 330
990 ÷ 5 = 198
990 ÷ 6 = 165
990 ÷ 9 = 110
990 ÷ 10 = 99
990 ÷ 11 = 90
990 ÷ 15 = 66
990 ÷ 18 = 55
990 ÷ 22 = 45
990 ÷ 30 = 33
Therefore, the factors of 990 are: 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, and 990.
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 990 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
990 ÷ 2 = 495
495 ÷ 3 = 165
165 ÷ 3 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1
The prime factors of 990 are 2, 3, 5, and 11.
The prime factorization of 990 is: 2 × 32 × 5 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 990 is divided by 2 to get 495.
Step 2: Now divide 495 by 3 to get 165.
Step 3: Then divide 165 by 3 to get 55.
Step 4: Divide 55 by 5 to get 11. Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 990 is: 2 × 32 × 5 × 11.
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 990: (1, 990), (2, 495), (3, 330), (5, 198), (6, 165), (9, 110), (10, 99), (11, 90), (15, 66), (18, 55), (22, 45), and (30, 33).
Negative factor pairs of 990: (-1, -990), (-2, -495), (-3, -330), (-5, -198), (-6, -165), (-9, -110), (-10, -99), (-11, -90), (-15, -66), (-18, -55), (-22, -45), and (-30, -33).
Common Mistakes and How to Avoid Them in Factors of 990
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 990, 1 and 990 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 990 consist of -1, -2, -3, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 990/1.5 = 660, 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 990 are prime numbers.
For example, 2, 3, 5, and 11 are the prime factors of 990, but it has other factors like 6, 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 990 as 2 × 3^2 × 5 × 11 and missing all the key factors.
Factors of 990 Examples
Problem 1
A theater has 990 seats. If each row has 9 seats, how many rows are there?
There are 110 rows.
Explanation
To find the number of rows, we need to divide the total seats by the number of seats per row.
990/9 = 110
Problem 2
A floor is rectangular, the width of the floor is 15 meters, and the total area is 990 square meters. Find the length?
66 meters.
Explanation
To find the length of the floor, we use the formula,
Area = length × width
990 = 15 × length
To find the value of length, we need to shift 15 to the left side.
990/15 = length
Length = 66.
Problem 3
A farmer has 990 apples and 18 baskets. How many apples will be in each basket?
Each basket will have 55 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
990/18 = 55
Problem 4
In a class, there are 990 students and 11 groups. How many students are there in each group?
There are 90 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
990/11 = 90
Problem 5
990 books need to be arranged in 33 shelves. How many books will go on each shelf?
Each of the shelves has 30 books.
Explanation
Divide total books by shelves.
990/33 = 30
FAQs on Factors of 990
1.What are the factors of 990?
2.Mention the prime factors of 990.
3.Is 990 a multiple of 11?
4.Mention the factor pairs of 990?
5.What is the square of 990?
Important Glossaries for Factors of 990
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 11 are prime factors of 990.
- 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 990 are (1, 990), (2, 495), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 990 is 2 × 32 × 5 × 11.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number.
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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.
