101 LearnersLast updated on August 5th, 2025
GCF of 240 and 90
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 240 and 90.
What is the GCF of 240 and 90?
The greatest common factor of 240 and 90 is 30. 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 240 and 90?
To find the GCF of 240 and 90, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 240 and 90 by Using Listing of Factors
Steps to find the GCF of 240 and 90 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
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 240 and 90: 1, 2, 3, 5, 6, 10, 15, 30.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 30.
The GCF of 240 and 90 is 30.
GCF of 240 and 90 Using Prime Factorization
To find the GCF of 240 and 90 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 240: 240 = 2 × 2 × 2 × 2 × 3 × 5 = 2⁴ × 3 × 5
Prime Factors of 90: 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 × 3 × 5
Step 3: Multiply the common prime factors. 2 × 3 × 5 = 30.
The Greatest Common Factor of 240 and 90 is 30.
GCF of 240 and 90 Using Division Method or Euclidean Algorithm Method
Find the GCF of 240 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 240 by 90. 240 ÷ 90 = 2 (quotient),
The remainder is calculated as 240 − (90×2) = 60.
The remainder is 60, not zero, so continue the process.
Step 2: Now divide the previous divisor (90) by the previous remainder (60).
Divide 90 by 60. 90 ÷ 60 = 1 (quotient), remainder = 90 − (60×1) = 30.
Step 3: Now divide the previous divisor (60) by the previous remainder (30). 60 ÷ 30 = 2 (quotient), remainder = 60 − (30×2) = 0.
The remainder is zero, the divisor will become the GCF.
The GCF of 240 and 90 is 30.
Common Mistakes and How to Avoid Them in GCF of 240 and 90
Finding the GCF of 240 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 240, students may mention 14, 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. Although it does not affect the GCF, it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with multiples. In that confusion, 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 the 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 240 and 90 Examples
Problem 1
A chef has 240 grams of flour and 90 grams of sugar. He wants to divide them into equal portions, with the largest possible number of grams in each portion. How many grams will be in each portion?
We should find the GCF of 240 and 90.
GCF of 240 and 90: 2 × 3 × 5 = 30.
There are 30 equal portions. 240 ÷ 30 = 8
90 ÷ 30 = 3
There will be 30 portions, and each portion will have 8 grams of flour and 3 grams of sugar.
Explanation
As the GCF of 240 and 90 is 30, the chef can make 30 portions. Now divide 240 and 90 by 30. Each portion gets 8 grams of flour and 3 grams of sugar.
Problem 2
A landscaper has 240 meters of garden hose and 90 meters of rope. He wants to cut them into the longest possible equal lengths without any leftover material. What should be the length of each piece?
GCF of 240 and 90: 2 × 3 × 5 = 30.
So each piece will be 30 meters long.
Explanation
There are 240 meters of garden hose and 90 meters of rope. To find the length of each piece, we should find the GCF of 240 and 90. Each piece will be 30 meters long.
Problem 3
A painter has 240 milliliters of red paint and 90 milliliters of blue paint. She wants to mix them into batches using the maximum equal volume for each batch. What should be the volume of each batch?
For calculating the maximum equal volume, we have to calculate the GCF of 240 and 90.
The GCF of 240 and 90: 2 × 3 × 5 = 30.
The volume of each batch is 30 milliliters.
Explanation
For calculating the maximum volume of each batch, we first need to calculate the GCF of 240 and 90, which is 30. The volume of each batch will be 30 milliliters.
Problem 4
A farmer has two fields, one 240 acres and the other 90 acres. He wants to divide them into the largest possible equal sections, with none left over. What should be the area of each section?
The farmer needs the largest section of land.
GCF of 240 and 90: 2 × 3 × 5 = 30.
The area of each section is 30 acres.
Explanation
To find the area of each section of the two fields, 240 acres and 90 acres, respectively, we have to find the GCF of 240 and 90, which is 30 acres. The area of each section is 30 acres.
Problem 5
If the GCF of 240 and ‘b’ is 30, and the LCM is 720, find ‘b’.
The value of ‘b’ is 90.
Explanation
GCF × LCM = product of the numbers 30 × 720 = 240 × b
21600 = 240b
b = 21600 ÷ 240 = 90
FAQs on the Greatest Common Factor of 240 and 90
1.What is the LCM of 240 and 90?
2.Is 240 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 90?
5.Are 240 and 90 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 240 and 90?
7.What are some fun ways kids in United States can practice GCF of 240 and 90 with numbers?
8.What role do numbers and GCF of 240 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 240 and 90 skills?
Important Glossaries for GCF of 240 and 90
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
- 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, 25, 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 90 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, 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 240 and 90 is 720.
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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.
