121 LearnersLast updated on May 26th, 2025
Factors of 90
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 90, how they are used in real life, and tips to learn them quickly.
What are the Factors of 90?
The numbers that divide 90 evenly are known as factors of 90. A factor of 90 is a number that divides the number without remainder. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Negative factors of 90: -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, and -90. Prime factors of 90: 2, 3, and 5. Prime factorization of 90: 2 × 3² × 5. The sum of factors of 90: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234
How to Find Factors of 90?
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 90. Identifying the numbers which are multiplied to get the number 90 is the multiplication method. Step 1: Multiply 90 by 1, 90 × 1 = 90. Step 2: Check for other numbers that give 90 after multiplying 2 × 45 = 90 3 × 30 = 90 5 × 18 = 90 6 × 15 = 90 9 × 10 = 90 Therefore, the positive factor pairs of 90 are: (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), (9, 10). 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 90 by 1, 90 ÷ 1 = 90. Step 2: Continue dividing 90 by the numbers until the remainder becomes 0. 90 ÷ 1 = 90 90 ÷ 2 = 45 90 ÷ 3 = 30 90 ÷ 5 = 18 90 ÷ 6 = 15 90 ÷ 9 = 10 Therefore, the factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 90 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. 90 ÷ 2 = 45 45 ÷ 3 = 15 15 ÷ 3 = 5 5 ÷ 5 = 1 The prime factors of 90 are 2, 3, and 5. The prime factorization of 90 is: 2 × 3² × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows - Step 1: Firstly, 90 is divided by 2 to get 45. Step 2: Now divide 45 by 3 to get 15. Step 3: Then divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 90 is: 2 × 3² × 5. 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 90: (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), and (9, 10). Negative factor pairs of 90: (-1, -90), (-2, -45), (-3, -30), (-5, -18), (-6, -15), and (-9, -10).
Common Mistakes and How to Avoid Them in Factors of 90
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 factors for every number. Always remember to include 1 and the number itself. For example, in factors of 90, 1 and 90 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 90 consist of -1, -2, -3, 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 90/1.5 = 60, 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 90 are prime numbers. For example, 2, 3, and 5 are the prime factors of 90, but it has other factors like 6, 15.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors. For example, not breaking 90 as 2 × 3² × 5 and missing all the key factors.
Factors of 90 Examples
Problem 1
There are 9 teams and 90 players. How will they divide the players equally?
Each team will get 10 players.
Explanation
To divide the players equally, we need to divide the total number of players by the number of teams. 90/9 = 10
Problem 2
A garden is rectangular, the length of the garden is 15 meters and the total area is 90 square meters. Find the width.
6 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 90 = 15 × width To find the value of the width, we need to shift 15 to the left side. 90/15 = width Width = 6.
Problem 3
There are 18 boxes and 90 chocolates. How many chocolates will be in each box?
Each box will have 5 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates by the boxes. 90/18 = 5
Problem 4
In a company, there are 90 employees, and 5 departments. How many employees are there in each department?
There are 18 employees in each department.
Explanation
Dividing the employees by the total departments, we will get the number of employees in each department. 90/5 = 18
Problem 5
90 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 18 books.
Explanation
Divide total books by shelves. 90/5 = 18
FAQs on Factors of 90
1.What are the factors of 90?
2.Mention the prime factors of 90.
3.Is 90 a multiple of 9?
4.Mention the factor pairs of 90.
5.What is the square of 90?
6.How can children in Qatar use numbers in everyday life to understand Factors of 90?
7.What are some fun ways kids in Qatar can practice Factors of 90 with numbers?
8.What role do numbers and Factors of 90 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 90 skills?
Important Glossaries for Factors of 90
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 90. 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 90 are (1, 90), (2, 45), etc. Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 90 is 2 × 3² × 5. Sum of factors: The total when all factors of a number are added together. For example, the sum of the factors of 90 is 234.
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About BrightChamps in Qatar
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.
