GCF of 12 and 80
2026-02-28 09:48 Diff
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Last updated on September 20, 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 80.

What is the GCF of 12 and 80?

The greatest common factor of 12 and 80 is 4. 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.

How to find the GCF of 12 and 80?

To find the GCF of 12 and 80, a few methods are described below 

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

GCF of 12 and 80 by Using Listing of factors

Steps to find the GCF of 12 and 80 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 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.

Step 2: Now, identify the common factors of them Common factors of 12 and 80: 1, 2, 4.

Step 3: Choose the largest factor The largest factor that both numbers have is 4.

The GCF of 12 and 80 is 4.

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GCF of 12 and 80 Using Prime Factorization

To find the GCF of 12 and 80 using 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 80: 80 = 2 x 2 x 2 x 2 x 5 = 2⁴ x 5

Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 = 2²

Step 3: Multiply the common prime factors 2² = 4.

The Greatest Common Factor of 12 and 80 is 4.

GCF of 12 and 80 Using Division Method or Euclidean Algorithm Method

Find the GCF of 12 and 80 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number

Here, divide 80 by 12 80 ÷ 12 = 6 (quotient)

The remainder is calculated as 80 − (12 × 6) = 8

The remainder is 8, not zero, so continue the process

Step 2: Now divide the previous divisor (12) by the previous remainder (8)

Divide 12 by 8 12 ÷ 8 = 1 (quotient), remainder = 12 − (8 × 1) = 4

Step 3: Now divide the previous divisor (8) by the previous remainder (4)

Divide 8 by 4 8 ÷ 4 = 2 (quotient), remainder = 8 − (4 × 2) = 0

The remainder is zero, the divisor will become the GCF.

The GCF of 12 and 80 is 4.

Common Mistakes and How to Avoid Them in GCF of 12 and 80

Finding GCF of 12 and 80 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 baker has 12 chocolate cupcakes and 80 vanilla cupcakes. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?

Okay, lets begin

We should find the GCF of 12 and 80 GCF of 12 and 80 2² = 4.

There are 4 equal groups 12 ÷ 4 = 3 80 ÷ 4 = 20

There will be 4 groups, and each group gets 3 chocolate cupcakes and 20 vanilla cupcakes.

Explanation

As the GCF of 12 and 80 is 4, the baker can make 4 groups.

Now divide 12 and 80 by 4.

Each group gets 3 chocolate cupcakes and 20 vanilla cupcakes.

Well explained 👍

Problem 2

A decorator has 12 red balloons and 80 blue balloons. She wants 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 80 2² = 4. So each row will have 4 balloons.

Explanation

There are 12 red and 80 blue balloons. To find the total number of balloons in each row, we should find the GCF of 12 and 80.

There will be 4 balloons in each row.

Well explained 👍

Problem 3

A tailor has 12 meters of red fabric and 80 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 12 and 80

The GCF of 12 and 80 2² = 4.

The fabric is 4 meters long.

Explanation

For calculating the longest length of the fabric, first, we need to calculate the GCF of 12 and 80, which is 4.

The length of each piece of the fabric will be 4 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 12 cm long and the other 80 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 80 2² = 4.

The longest length of each piece is 4 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 12 cm and 80 cm, respectively, we have to find the GCF of 12 and 80, which is 4 cm.

The longest length of each piece is 4 cm.

Well explained 👍

Problem 5

If the GCF of 12 and ‘a’ is 4, and the LCM is 240. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 80.

Explanation

GCF x LCM = product of the numbers

4 × 240 = 12 × a

960 = 12a

a = 960 ÷ 12 = 80

Well explained 👍

FAQs on the Greatest Common Factor of 12 and 80

1.What is the LCM of 12 and 80?

The LCM of 12 and 80 is 240.

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 80?

The prime factorization of 80 is 2⁴ × 5.

5.Are 12 and 80 prime numbers?

No, 12 and 80 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 12 and 80

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
  • 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 12 is divided by 7, the remainder is 5, and the quotient is 1.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 80 is 240.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 80 is 4, as it is their largest common factor that divides the numbers completely.

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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.