102 LearnersLast updated on August 5th, 2025
GCF of 24 and 90
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 24 and 90.
What is the GCF of 24 and 90?
The greatest common factor of 24 and 90 is 6. The largest divisor of two or more numbers is called the GCF of the numbers. 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 24 and 90?
To find the GCF of 24 and 90, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 24 and 90 by Using Listing of factors
Steps to find the GCF of 24 and 90 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Step 2: Now, identify the common factors of them Common factors of 24 and 90: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 24 and 90 is 6.
GCF of 24 and 90 Using Prime Factorization
To find the GCF of 24 and 90 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2³ x 3
Prime Factors of 90: 90 = 2 x 3 x 3 x 5 = 2 x 3² x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3 = 2¹ x 3¹
Step 3: Multiply the common prime factors 2¹ x 3¹ = 2 x 3 = 6.
The Greatest Common Factor of 24 and 90 is 6.
GCF of 24 and 90 Using Division Method or Euclidean Algorithm Method
Find the GCF of 24 and 90 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 24 90 ÷ 24 = 3 (quotient),
The remainder is calculated as 90 − (24×3) = 18
The remainder is 18, not zero, so continue the process
Step 2: Now divide the previous divisor (24) by the previous remainder (18)
Divide 24 by 18 24 ÷ 18 = 1 (quotient), remainder = 24 − (18×1) = 6
Step 3: Continue the process. Now divide the previous divisor (18) by the previous remainder (6) 18 ÷ 6 = 3 (quotient), remainder = 18 − (6×3) = 0
The remainder is zero, so the divisor at this step is the GCF.
The GCF of 24 and 90 is 6.
Common Mistakes and How to Avoid Them in GCF of 24 and 90
Finding GCF of 24 and 90 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 24, students may mention 10 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 24 and 90 Examples
Problem 1
A florist has 24 roses and 90 tulips. She wants to create bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find GCF of 24 and 90 GCF of 24 and 90 2 x 3 = 6.
There are 6 flowers in each bouquet. 24 ÷ 6 = 4
90 ÷ 6 = 15
There will be 6 bouquets, and each bouquet gets 4 roses and 15 tulips.
Explanation
As the GCF of 24 and 90 is 6, the florist can make bouquets with 6 flowers each. Now divide 24 and 90 by 6. Each bouquet gets 4 roses and 15 tulips.
Problem 2
A farmer has 24 apple trees and 90 orange trees. He wants to arrange them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 24 and 90 2 x 3 = 6.
So each row will have 6 trees.
Explanation
There are 24 apple trees and 90 orange trees. To find the total number of trees in each row, we should find the GCF of 24 and 90. There will be 6 trees in each row.
Problem 3
A chef has 24 kg of flour and 90 kg of sugar. She wants to package them into bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 24 and 90
The GCF of 24 and 90
2 x 3 = 6.
Each bag will weigh 6 kg.
Explanation
For calculating the largest weight of each bag, first we need to calculate the GCF of 24 and 90 which is 6. The weight of each bag will be 6 kg.
Problem 4
A gardener has two pieces of land, one 24 meters wide and the other 90 meters wide. He wants to divide them into the longest possible equal sections. What should be the width of each section?
The gardener needs the longest section width GCF of 24 and 90 2 x 3 = 6.
The longest width of each section is 6 meters.
Explanation
To find the longest width of each section of the two pieces of land, 24 meters and 90 meters wide respectively. We have to find the GCF of 24 and 90, which is 6 meters. The longest width of each section is 6 meters.
Problem 5
If the GCF of 24 and ‘b’ is 6, and the LCM is 360. Find ‘b’.
The value of ‘b’ is 90.
Explanation
GCF x LCM = product of the numbers 6 x 360 = 24 x b
2160 = 24b
b = 2160 ÷ 24 = 90
FAQs on the Greatest Common Factor of 24 and 90
1.What is the LCM of 24 and 90?
2.Is 24 divisible by 3?
3.What will be the GCF of 24 and any multiple of 24?
4.What is the prime factorization of 90?
5.Are 24 and 90 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 24 and 90?
7.What are some fun ways kids in United States can practice GCF of 24 and 90 with numbers?
8.What role do numbers and GCF of 24 and 90 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 24 and 90 skills?
Important Glossaries for GCF of 24 and 90
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 4, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.
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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.
