Last updated on July 30th, 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 to schedule events. In this topic, we will learn about the GCF of 6 and 12.
The greatest common factor of 6 and 12 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 6 and 12, a few methods are described below
Steps to find the GCF of 6 and 12 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 6 = 1, 2, 3, 6.
Factors of 12 = 1, 2, 3, 4, 6, 12.
Step 2: Now, identify the common factors of them. Common factors of 6 and 12: 1, 2, 3, 6.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 6.
The GCF of 6 and 12 is 6.
To find the GCF of 6 and 12 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 6: 6 = 2 x 3
Prime Factors of 12: 12 = 2 x 2 x 3
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 6 and 12 is 6.
Find the GCF of 6 and 12 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, 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 6 and 12 is 6.
Finding GCF of 6 and 12 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 6 kilograms of potatoes and 12 kilograms of carrots. He wants to divide them into equal portions with the largest possible weight in each portion. How many kilograms will each portion weigh?
We should find the GCF of 6 and 12 GCF of 6 and 12
2 x 3 = 6.
There are 6 equal portions
6 ÷ 6 = 1
12 ÷ 6 = 2
There will be 6 portions, and each portion will have 1 kilogram of potatoes and 2 kilograms of carrots.
As the GCF of 6 and 12 is 6, the chef can make 6 portions.
Now divide 6 and 12 by 6.
Each portion will have 1 kilogram of potatoes and 2 kilograms of carrots.
A florist has 6 roses and 12 lilies. She wants to arrange them in bouquets with the same number of flowers in each, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?
GCF of 6 and 12
2 x 3 = 6.
So each bouquet will have 6 flowers.
There are 6 roses and 12 lilies. To find the total number of flowers in each bouquet, we should find the GCF of 6 and 12. There will be 6 flowers in each bouquet.
A gardener has 6 meters of red hose and 12 meters of green hose. She wants to cut both hoses into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 6 and 12
The GCF of 6 and 12
2 x 3 = 6.
The hose is 6 meters long.
For calculating the longest length of the hose first we need to calculate the GCF of 6 and 12 which is 6. The length of each piece of the hose will be 6 meters.
A seamstress has two pieces of fabric, one 6 meters long and the other 12 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The seamstress needs the longest piece of fabric GCF of 6 and 12
2 x 3 = 6.
The longest length of each piece is 6 meters.
To find the longest length of each piece of the two pieces of fabric, 6 meters and 12 meters, respectively. We have to find the GCF of 6 and 12, which is 6 meters. The longest length of each piece is 6 meters.
If the GCF of 6 and ‘b’ is 6, and the LCM is 12. Find ‘b’.
The value of ‘b’ is 12.
GCF x LCM = product of the numbers
6 × 12 = 6 × b
72 = 6b
b = 72 ÷ 6 = 12
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.