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 12 and 36.
The greatest common factor of 12 and 36 is 12. The largest divisor of two or more numbers is called the GCF. 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 36, a few methods are described below -
Steps to find the GCF of 12 and 36 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 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 2: Now, identify the common factors of them Common factors of 12 and 36: 1, 2, 3, 4, 6, 12.
Step 3: Choose the largest factor
The largest factor that both numbers have is 12.
The GCF of 12 and 36 is 12.
To find the GCF of 12 and 36 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 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 3 = 2² x 3
Step 3: Multiply the common prime factors 2² x 3 = 4 x 3 = 12.
The Greatest Common Factor of 12 and 36 is 12.
Find the GCF of 12 and 36 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 36 by 12 36 ÷ 12 = 3 (quotient), remainder = 36 − (12 x 3) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 12 and 36 is 12.
Finding GCF of 12 and 36 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A farmer has 12 apples and 36 oranges. He wants to pack them into equal baskets, with the largest number of items in each basket. How many items will be in each basket?
We should find the GCF of 12 and 36 GCF of 12 and 36 2² x 3 = 4 x 3 = 12.
There are 12 equal baskets. 12 ÷ 12 = 1 36 ÷ 12 = 3
There will be 12 baskets, and each basket gets 1 apple and 3 oranges.
As the GCF of 12 and 36 is 12, the farmer can make 12 baskets. Now divide 12 and 36 by 12. Each basket gets 1 apple and 3 oranges.
A decorator has 12 red balloons and 36 blue balloons. They want to arrange them in rows with the same number of balloons in each row, using the largest possible number of balloons per row. How many balloons will be in each row?
GCF of 12 and 36 2² x 3 = 4 x 3 = 12
. So each row will have 12 balloons.
There are 12 red and 36 blue balloons. To find the total number of balloons in each row, we should find the GCF of 12 and 36. There will be 12 balloons in each row.
A weaver has 12 meters of cotton thread and 36 meters of wool thread. She wants to cut both threads 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 36
The GCF of 12 and 36
2² x 3 = 4 x 3 = 12.
The thread is 12 meters long.
For calculating the longest length of the thread, we first need to calculate the GCF of 12 and 36, which is 12. The length of each piece of the thread will be 12 meters.
A carpenter has two wooden planks, one 12 cm long and the other 36 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 36
2² x 3 = 4 x 3 = 12.
The longest length of each piece is 12 cm.
To find the longest length of each piece of the two wooden planks, 12 cm and 36 cm, respectively, we have to find the GCF of 12 and 36, which is 12 cm. The longest length of each piece is 12 cm.
If the GCF of 12 and ‘a’ is 12, and the LCM is 36. Find ‘a’.
The value of ‘a’ is 36.
GCF x LCM = product of the numbers 12 x 36 = 12 x a
432 = 12a
a = 432 ÷ 12 = 36
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.