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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 12 and 54.
The greatest common factor of 12 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 12 and 54, a few methods are described below:
Steps to find the GCF of 12 and 54 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: Now, identify the common factors of them. Common factors of 12 and 54: 1, 2, 3, 6.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 6.
The GCF of 12 and 54 is 6.
To find the GCF of 12 and 54 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 12: 12 = 2 × 2 × 3 = 2² × 3
Prime Factors of 54: 54 = 2 × 3 × 3 × 3 = 2 × 3³
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 × 3 = 2 × 3
Step 3: Multiply the common prime factors 2 × 3 = 6.
The Greatest Common Factor of 12 and 54 is 6.
Find the GCF of 12 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 12 54 ÷ 12 = 4 (quotient), The remainder is calculated as 54 − (12 × 4) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (6)
Divide 12 by 6 12 ÷ 6 = 2 (quotient), remainder = 12 − (6 × 2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 54 is 6.
Finding the GCF of 12 and 54 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
A chef has 12 apples and 54 oranges. He wants to create fruit baskets with the largest possible number of apples and oranges in each basket. How many apples and oranges will be in each basket?
We should find the GCF of 12 and 54 GCF of 12 and 54
2 × 3 = 6.
There are 6 equal groups
12 ÷ 6 = 2
54 ÷ 6 = 9
There will be 6 baskets, with each basket containing 2 apples and 9 oranges.
As the GCF of 12 and 54 is 6, the chef can make 6 baskets.
Now divide 12 and 54 by 6.
Each basket gets 2 apples and 9 oranges.
A music teacher has 12 flutes and 54 violins. She wants to arrange them in rows with the same number of instruments in each row, using the largest possible number of instruments per row. How many instruments will be in each row?
GCF of 12 and 54 2 × 3 = 6. So each row will have 6 instruments.
There are 12 flutes and 54 violins. To find the total number of instruments in each row, we should find the GCF of 12 and 54. There will be 6 instruments in each row.
A ribbon maker has 12 meters of gold ribbon and 54 meters of silver ribbon. She wants to cut both ribbons 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 12 and 54
The GCF of 12 and 54
2 × 3 = 6.
The ribbon is 6 meters long.
For calculating the longest length of the ribbon first, we need to calculate the GCF of 12 and 54, which is 6. The length of each piece of the ribbon will be 6 meters.
A farmer has two pieces of land, one 12 hectares and the other 54 hectares. He wants to divide them into the longest possible equal plots without any land left over. What should be the size of each plot?
The farmer needs the longest piece of land GCF of 12 and 54
2 × 3 = 6.
The longest size of each plot is 6 hectares.
To find the longest size of each plot of the two pieces of land, 12 hectares and 54 hectares, respectively, we have to find the GCF of 12 and 54, which is 6 hectares.
The longest size of each plot is 6 hectares.
If the GCF of 12 and ‘b’ is 6, and the LCM is 108, find ‘b’.
The value of ‘b’ is 54.
GCF × LCM = product of the numbers
6 × 108 = 12 × b
648 = 12b
b = 648 ÷ 12 = 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.