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127 LearnersLast updated on December 11, 2025
GCF of 24 and 228
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 228.
What is the GCF of 24 and 228?
The greatest common factor of 24 and 228 is 12.
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 24 and 228?
To find the GCF of 24 and 228, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 24 and 228 by Using Listing of factors
Steps to find the GCF of 24 and 228 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 228 = 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228.
Step 2: Now, identify the common factors of them Common factors of 24 and 228: 1, 2, 3, 4, 6, 12.
Step 3: Choose the largest factor The largest factor that both numbers have is 12.
The GCF of 24 and 228 is 12.
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GCF of 24 and 228 Using Prime Factorization
To find the GCF of 24 and 228 using the 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 228: 228 = 2 x 2 x 3 x 19 = 2² x 3 x 19.
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 = 2² x 3.
Step 3: Multiply the common prime factors 2² x 3 = 4 × 3 = 12.
The Greatest Common Factor of 24 and 228 is 12.
GCF of 24 and 228 Using Division Method or Euclidean Algorithm Method
Find the GCF of 24 and 228 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 228 by 24 228 ÷ 24 = 9 (quotient), The remainder is calculated as 228 − (24×9) = 12 The remainder is 12, not zero, so continue the process.
Step 2: Now divide the previous divisor (24) by the previous remainder (12) Divide 24 by 12 24 ÷ 12 = 2 (quotient), remainder = 24 − (12×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 24 and 228 is 12.
Common Mistakes and How to Avoid Them in GCF of 24 and 228
Finding GCF of 24 and 228 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 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, 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 the GCF of two numbers will always be an even number.
However, it's not true; 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 228 Examples
Problem 1
A farmer has 24 apple trees and 228 orange trees. He wants to plant them in rows with the largest number of trees in each row. How many trees will be in each row?
We should find the GCF of 24 and 228 GCF of 24 and 228,
2² x 3 = 4 x 3 = 12.
There are 12 trees per row 24 ÷ 12 = 2 228 ÷ 12 = 19
There will be 12 trees in each row.
Explanation
As the GCF of 24 and 228 is 12, the farmer can plant 12 trees per row.
Now divide 24 and 228 by 12 to determine how many rows he'll have.
Problem 2
A company has 24 old computers and 228 new computers. They want to distribute them in groups with the same number of computers in each group, using the largest possible number of computers per group. How many computers will be in each group?
GCF of 24 and 228 2² x 3 = 4 × 3 = 12.
So each group will have 12 computers.
Explanation
There are 24 old and 228 new computers.
To find the total number of computers in each group, we should find the GCF of 24 and 228.
There will be 12 computers in each group.
Problem 3
A chef has 24 liters of olive oil and 228 liters of vegetable oil. She wants to pour them into bottles of equal capacity, using the largest possible capacity. What should be the capacity of each bottle?
For calculating the largest equal capacity, we have to calculate the GCF of 24 and 228.
The GCF of 24 and 228 = 2² x 3 = 4 × 3 = 12.
The capacity of each bottle will be 12 liters.
Explanation
For calculating the largest capacity of the bottles, we first need to calculate the GCF of 24 and 228, which is 12.
The capacity of each bottle will be 12 liters.
Problem 4
A contractor has two cables, one 24 meters long and the other 228 meters long. He wants to cut them into the longest possible equal pieces, without any cable left over. What should be the length of each piece?
The contractor needs the longest piece of cable GCF of 24 and 228 = 2² x 3 = 4 × 3 = 12.
The longest length of each piece is 12 meters.
Explanation
To find the longest length of each piece of the two cables, 24 meters and 228 meters, respectively, we have to find the GCF of 24 and 228, which is 12 meters.
The longest length of each piece is 12 meters.
Problem 5
If the GCF of 24 and โaโ is 12, and the LCM is 456. Find โaโ.
The value of ‘a’ is 228.
Explanation
GCF x LCM = product of the numbers
12 × 456 = 24 × a
5472 = 24a
a = 5472 ÷ 24 = 228
FAQs on the Greatest Common Factor of 24 and 228
1.What is the LCM of 24 and 228?
2.Is 24 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 228?
5.Are 24 and 228 prime numbers?
Important Glossaries for GCF of 24 and 228
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 228 is 456.
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.
