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102 LearnersLast updated on September 20, 2025
GCF of 90 and 18
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 90 and 18.
What is the GCF of 90 and 18?
The greatest common factor of 90 and 18 is 18. The largest divisor of two or more numbers is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 90 and 18?
To find the GCF of 90 and 18, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 90 and 18 by Using Listing of Factors
Steps to find the GCF of 90 and 18 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Factors of 18 = 1, 2, 3, 6, 9, 18.
Step 2: Now, identify the common factors of them Common factors of 90 and 18: 1, 2, 3, 6, 9, 18.
Step 3: Choose the largest factor The largest factor that both numbers have is 18.
The GCF of 90 and 18 is 18.
GCF of 90 and 18 Using Prime Factorization
To find the GCF of 90 and 18 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 90: 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5
Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3²
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 3 × 3 = 2 × 3²
Step 3: Multiply the common prime factors 2 × 3² = 2 × 9 = 18.
The Greatest Common Factor of 90 and 18 is 18.
GCF of 90 and 18 Using Division Method or Euclidean Algorithm Method
Find the GCF of 90 and 18 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 90 by 18 90 ÷ 18 = 5 (quotient), The remainder is calculated as 90 − (18×5) = 0
The remainder is zero, so the divisor becomes the GCF.
The GCF of 90 and 18 is 18.
Common Mistakes and How to Avoid Them in GCF of 90 and 18
Finding GCF of 90 and 18 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 90, students may mention 8, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 90 and 18 Examples
Problem 1
A florist has 90 roses and 18 lilies. She wants to create floral arrangements with the largest number of flowers in each arrangement, ensuring each arrangement has an equal number of roses and lilies. How many flowers will be in each arrangement?
We should find the GCF of 90 and 18 GCF of 90 and 18
2 × 3² = 2 × 9 = 18.
There are 18 equal arrangements 90 ÷ 18 = 5 18 ÷ 18 = 1
There will be 18 arrangements, and each arrangement gets 5 roses and 1 lily.
Explanation
As the GCF of 90 and 18 is 18, the florist can make 18 arrangements.
Now divide 90 and 18 by 18.
Each arrangement gets 5 roses and 1 lily.
Problem 2
A caterer has 90 plates and 18 bowls. They want to set the tables using the largest possible number of plates and bowls per table, making sure each table has the same number of plates and bowls. How many will be on each table?
GCF of 90 and 18 2 × 3² = 2 × 9 = 18.
So each table will have 18 items.
Explanation
There are 90 plates and 18 bowls.
To find the total number of items on each table, we should find the GCF of 90 and 18.
There will be 18 items on each table.
Problem 3
A seamstress has 90 meters of cotton fabric and 18 meters of silk fabric. She wants to cut them into equal lengths with the longest possible length for each piece. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 90 and 18
The GCF of 90 and 18 2 × 3² = 2 × 9 = 18.
The fabric is 18 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 90 and 18, which is 18.
The length of each piece of fabric will be 18 meters.
Problem 4
A carpenter has two wooden planks, one 90 cm long and the other 18 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 90 and 18
2 × 3² = 2 × 9 = 18.
The longest length of each piece is 18 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 90 cm and 18 cm, respectively.
We have to find the GCF of 90 and 18, which is 18 cm.
The longest length of each piece is 18 cm.
Problem 5
If the GCF of 90 and ‘a’ is 18, and the LCM is 180. Find ‘a’.
The value of ‘a’ is 36.
Explanation
GCF × LCM = product of the numbers
18 × 180 = 90 × a
3240 = 90a
a = 3240 ÷ 90 = 36
FAQs on the Greatest Common Factor of 90 and 18
1.What is the LCM of 90 and 18?
2.Is 90 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 18?
5.Are 90 and 18 prime numbers?
Important Glossaries for GCF of 90 and 18
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- Prime Factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 90 is 2 × 3² × 5.
- Common Factor: A number that divides two or more numbers without leaving a remainder. For example, 18 is a common factor of 90 and 18.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 90 and 18 is 18.
- Even Number: A number that is divisible by 2. For example, 90 is an even 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.
