GCF of 12 and 36
2026-02-28 11:16 Diff
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Last updated on August 5, 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.

What is 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.

How to find the GCF of 12 and 36?

To find the GCF of 12 and 36, a few methods are described below -

  • Listing Factors
  • Prime Factorization
  • Long Division Method / by Euclidean Algorithm

GCF of 12 and 36 by Using Listing of factors

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.

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GCF of 12 and 36 Using Prime Factorization

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.

GCF of 12 and 36 Using Division Method or Euclidean Algorithm Method

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.

Common Mistakes and How to Avoid Them in GCF of 12 and 36

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.

Problem 1

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?

Okay, lets begin

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.

Explanation

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.

Well explained 👍

Problem 2

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?

Okay, lets begin

GCF of 12 and 36 2² x 3 = 4 x 3 = 12

. So each row will have 12 balloons.

Explanation

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.

Well explained 👍

Problem 3

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?

Okay, lets begin

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.

Explanation

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.

Well explained 👍

Problem 4

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?

Okay, lets begin

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.

Explanation

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.

Well explained 👍

Problem 5

If the GCF of 12 and ‘a’ is 12, and the LCM is 36. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 36.

Explanation

GCF x LCM = product of the numbers 12 x 36 = 12 x a

432 = 12a

a = 432 ÷ 12 = 36

Well explained 👍

FAQs on the Greatest Common Factor of 12 and 36

1.What is the LCM of 12 and 36?

The LCM of 12 and 36 is 36.

2.Is 12 divisible by 2?

Yes, 12 is divisible by 2 because it is an even number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 36?

The prime factorization of 36 is 2² x 3².

5.Are 12 and 36 prime numbers?

No, 12 and 36 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 12 and 36

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
  • Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 12 are 2 and 3.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 36 is 36.

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Hiralee Lalitkumar Makwana

About the Author

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.

Fun Fact

: She loves to read number jokes and games.