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 24 and 54.
The greatest common factor of 24 and 54 is 6. 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 24 and 54, a few methods are described below:
Steps to find the GCF of 24 and 54 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 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: Now, identify the common factors of them Common factors of 24 and 54: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 24 and 54 is 6.
To find the GCF of 24 and 54 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 54: 54 = 2 x 3 x 3 x 3 = 2 x 3³
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 x 3
Step 3: Multiply the common prime factors 2 x 3 = 6.
The Greatest Common Factor of 24 and 54 is 6.
Find the GCF of 24 and 54 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 54 by 24 54 ÷ 24 = 2 (quotient),
The remainder is calculated as 54 − (24×2) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (24) by the previous remainder (6)
Divide 24 by 6 24 ÷ 6 = 4 (quotient), remainder = 24 − (6×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 24 and 54 is 6.
Finding the GCF of 24 and 54 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A teacher has 24 notebooks and 54 pens. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 24 and 54 GCF of 24 and 54
2 x 3 = 6.
There are 6 equal groups
24 ÷ 6 = 4
54 ÷ 6 = 9
There will be 6 groups, and each group gets 4 notebooks and 9 pens.
As the GCF of 24 and 54 is 6, the teacher can make 6 groups.
Now divide 24 and 54 by 6.
Each group gets 4 notebooks and 9 pens.
A school has 24 red flags and 54 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 24 and 54 2 x 3 = 6. So each row will have 6 flags.
There are 24 red and 54 blue flags. To find the total number of flags in each row, we should find the GCF of 24 and 54. There will be 6 flags in each row.
A tailor has 24 meters of green fabric and 54 meters of yellow fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 24 and 54
The GCF of 24 and 54
2 x 3 = 6.
The fabric is 6 meters long.
For calculating the longest length of the fabric, first, we need to calculate the GCF of 24 and 54, which is 6. The length of each piece of fabric will be 6 meters.
A carpenter has two wooden beams, one 24 cm long and the other 54 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 24 and 54
2 x 3 = 6.
The longest length of each piece is 6 cm.
To find the longest length of each piece of the two wooden beams, 24 cm and 54 cm, respectively, we have to find the GCF of 24 and 54, which is 6 cm. The longest length of each piece is 6 cm.
If the GCF of 24 and ‘b’ is 6, and the LCM is 216. Find ‘b’.
The value of ‘b’ is 54.
GCF x LCM = product of the numbers
6 × 216 = 24 × b
1296 = 24b
b = 1296 ÷ 24 = 54
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.