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 to schedule events. In this topic, we will learn about the GCF of 10 and 12.
The greatest common factor of 10 and 12 is 2. 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 10 and 12, a few methods are described below -
Steps to find the GCF of 10 and 12 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 10 = 1, 2, 5, 10.
Factors of 12 = 1, 2, 3, 4, 6, 12.
Step 2: Now, identify the common factors of them Common factors of 10 and 12: 1, 2.
Step 3: Choose the largest factor
The largest factor that both numbers have is 2.
The GCF of 10 and 12 is 2.
To find the GCF of 10 and 12 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 10: 10 = 2 x 5
Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3
Step 2: Now, identify the common prime factors
The common prime factor is: 2
Step 3: Multiply the common prime factors
The Greatest Common Factor of 10 and 12 is 2.
Find the GCF of 10 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 10 12 ÷ 10 = 1 (quotient),
The remainder is calculated as 12−(10×1)=2
The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (10) by the previous remainder (2)
Divide 10 by 2 10 ÷ 2 = 5 (quotient), remainder = 10−(2×5)=0
The remainder is zero, the divisor will become the GCF.
The GCF of 10 and 12 is 2.
Finding GCF of 10 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 gardener has 10 tulips and 12 roses. She wants to group them into equal flower arrangements, with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 10 and 12 GCF of 10 and 12 2
There are 2 equal groups 10 ÷ 2 = 5 12 ÷ 2 = 6
There will be 2 groups, and each group gets 5 tulips and 6 roses.
As the GCF of 10 and 12 is 2, the gardener can make 2 groups.
Now divide 10 and 12 by 2.
Each group gets 5 tulips and 6 roses.
A party planner has 10 red balloons and 12 blue balloons. They want to arrange them in clusters with the same number of balloons in each cluster, using the largest possible number of balloons per cluster. How many balloons will be in each cluster?
GCF of 10 and 12 2
So each cluster will have 2 balloons.
There are 10 red and 12 blue balloons.
To find the total number of balloons in each cluster, we should find the GCF of 10 and 12.
There will be 2 balloons in each cluster.
A tailor has 10 meters of red fabric and 12 meters of blue 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 10 and 12
The GCF of 10 and 12 2
The fabric is 2 meters long.
For calculating the longest length of the fabric, first, we need to calculate the GCF of 10 and 12, which is 2.
The length of each piece of fabric will be 2 meters.
A carpenter has two wooden planks, one 10 cm long and the other 12 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 10 and 12 2
The longest length of each piece is 2 cm.
To find the longest length of each piece of the two wooden planks, 10 cm and 12 cm, respectively, we have to find the GCF of 10 and 12, which is 2 cm.
The longest length of each piece is 2 cm.
If the GCF of 10 and ‘b’ is 2, and the LCM is 60. Find ‘b’.
The value of ‘b’ is 12.
GCF × LCM = product of the numbers 2 × 60 = 10 × b
120 = 10b
b = 120 ÷ 10 = 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.