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 27.
The greatest common factor of 12 and 27 is 3. The largest divisor of two or more numbers is called the GCF of the numbers. 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 27, a few methods are described below:
Steps to find the GCF of 12 and 27 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 27 = 1, 3, 9, 27.
Step 2: Now, identify the common factors of them. Common factors of 12 and 27: 1, 3.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 3.
The GCF of 12 and 27 is 3.
To find the GCF of 12 and 27 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3 Prime Factors of 27: 27 = 3 x 3 x 3 = 3³
Step 2: Now, identify the common prime factors. The common prime factors are: 3
Step 3: Multiply the common prime factors 3 = 3. The Greatest Common Factor of 12 and 27 is 3.
Find the GCF of 12 and 27 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 12 27 ÷ 12 = 2 (quotient),
The remainder is calculated as 27 − (12×2) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (3)
Divide 12 by 3 12 ÷ 3 = 4 (quotient), remainder = 12 − (3×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 27 is 3.
Finding GCF of 12 and 27 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A baker has 12 chocolate muffins and 27 vanilla muffins. She wants to arrange them in trays with the largest number of muffins in each tray. How many muffins will be in each tray?
We should find the GCF of 12 and 27 GCF of 12 and 27 3.
There are 3 equal trays
12 ÷ 3 = 4
27 ÷ 3 = 9
There will be 3 trays, and each tray gets 4 chocolate muffins and 9 vanilla muffins.
As the GCF of 12 and 27 is 3, the baker can make 3 trays.
Now divide 12 and 27 by 3.
Each tray gets 4 chocolate muffins and 9 vanilla muffins.
A farmer has 12 apple trees and 27 orange trees. He wants to arrange them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 12 and 27 3. So each row will have 3 trees.
There are 12 apple trees and 27 orange trees.
To find the total number of trees in each row, we should find the GCF of 12 and 27.
There will be 3 trees in each row.
A tailor has 12 meters of silk fabric and 27 meters of cotton 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 12 and 27
The GCF of 12 and 27 3.
The fabric is 3 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 12 and 27 which is 3. The length of each piece of the fabric will be 3 meters.
A carpenter has two wooden planks, one 12 cm long and the other 27 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 12 and 27 3. The longest length of each piece is 3 cm.
To find the longest length of each piece of the two wooden planks, 12 cm and 27 cm, respectively. We have to find the GCF of 12 and 27, which is 3 cm. The longest length of each piece is 3 cm.
If the GCF of 12 and ‘a’ is 3, and the LCM is 108. Find ‘a’.
The value of ‘a’ is 27.
GCF x LCM = product of the numbers
3 × 108 = 12 × a
324 = 12a
a = 324 ÷ 12 = 27
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.