102 LearnersLast updated on August 5th, 2025
GCF of 27 and 24
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 27 and 24.
What is the GCF of 27 and 24?
The greatest common factor of 27 and 24 is 3. 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 27 and 24?
To find the GCF of 27 and 24, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 27 and 24 by Using Listing of Factors
Steps to find the GCF of 27 and 24 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 27 = 1, 3, 9, 27.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Step 2: Now, identify the common factors of them.
Common factors of 27 and 24: 1, 3.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 3.
The GCF of 27 and 24 is 3.
GCF of 27 and 24 Using Prime Factorization
To find the GCF of 27 and 24 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 27: 27 = 3 x 3 x 3 = 3^3
Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2^3 x 3
Step 2: Now, identify the common prime factors.
The common prime factor is: 3
Step 3: Multiply the common prime factors 3 = 3.
The Greatest Common Factor of 27 and 24 is 3.
GCF of 27 and 24 Using Division Method or Euclidean Algorithm Method
Find the GCF of 27 and 24 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 27 by 24 27 ÷ 24 = 1 (quotient), The remainder is calculated as 27 − (24×1) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (24) by the previous remainder (3)
Divide 24 by 3 24 ÷ 3 = 8 (quotient), remainder = 24 − (3×8) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 27 and 24 is 3.
Common Mistakes and How to Avoid Them in GCF of 27 and 24
Finding GCF of 27 and 24 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 27, students may mention 5, 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 27 and 24 Examples
Problem 1
A chef has 27 apples and 24 oranges. She wants to pack them into bags with the largest number of fruits in each bag. How many fruits will be in each bag?
We should find the GCF of 27 and 24 GCF of 27 and 24 is 3.
There are 3 fruits in each bag.
27 ÷ 3 = 9
24 ÷ 3 = 8
There will be 3 fruits in each bag, with 9 bags of apples and 8 bags of oranges.
Explanation
As the GCF of 27 and 24 is 3, the chef can pack 3 fruits per bag.
Now divide 27 and 24 by 3 to find the number of bags.
Problem 2
A farmer has 27 cows and 24 sheep. He wants to arrange them in groups with the same number of animals in each group, using the largest possible number of animals per group. How many animals will be in each group?
GCF of 27 and 24 is 3. So each group will have 3 animals.
Explanation
There are 27 cows and 24 sheep.
To find the total number of animals in each group, we should find the GCF of 27 and 24.
There will be 3 animals in each group.
Problem 3
A baker has 27 kilograms of flour and 24 kilograms of sugar. He wants to divide both into portions of equal weight, using the heaviest possible weight. What should be the weight of each portion?
For calculating the heaviest equal weight, we have to calculate the GCF of 27 and 24
The GCF of 27 and 24 is 3.
The portion is 3 kilograms.
Explanation
For calculating the heaviest portion, we first need to calculate the GCF of 27 and 24, which is 3. The weight of each portion will be 3 kilograms.
Problem 4
A company has two batches of cables, one 27 meters long and the other 24 meters long. They want to cut them into the longest possible equal pieces, without any cable left over. What should be the length of each piece?
The company needs the longest piece of cable GCF of 27 and 24 is 3.
The longest length of each piece is 3 meters.
Explanation
To find the longest length of each piece of the two batches of cables, 27 meters and 24 meters, respectively, we have to find the GCF of 27 and 24, which is 3 meters.
The longest length of each piece is 3 meters.
Problem 5
If the GCF of 27 and ‘b’ is 3, and the LCM is 216. Find ‘b’.
The value of ‘b’ is 24.
Explanation
GCF x LCM = product of the numbers
3 × 216 = 27 × b
648 = 27b
b = 648 ÷ 27 = 24
FAQs on the Greatest Common Factor of 27 and 24
1.What is the LCM of 27 and 24?
2.Is 27 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 24?
5.Are 27 and 24 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 27 and 24?
7.What are some fun ways kids in United Kingdom can practice GCF of 27 and 24 with numbers?
8.What role do numbers and GCF of 27 and 24 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 27 and 24 skills?
Important Glossaries for GCF of 27 and 24
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 11 is divided by 4, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 9 and 12 is 36.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 27 and 24 will be 3, as it is their largest common factor that divides the numbers completely.
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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.
