Last updated on August 5th, 2025
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.
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.
To find the GCF of 27 and 24, a few methods are described below:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 27 and ‘b’ is 3, and the LCM is 216. Find ‘b’.
The value of ‘b’ is 24.
GCF x LCM = product of the numbers
3 × 216 = 27 × b
648 = 27b
b = 648 ÷ 27 = 24
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.
: She loves to read number jokes and games.