GCF of 8 and 12
2026-02-28 08:28 Diff
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Last updated on August 5, 2025

The GCF of any two or more numbers is the greatest common factor among the given numbers. In daily life, GCF helps in easy grouping of items and designing arrangements. In this topic, we will learn about the GCF of 8 and 12 and the mistakes and tips related to it.

What is the GCF of 8 and 12

The largest common factor of 8 and 12 is the GCF. Here, the GCF of 8 and 12 is 4. GCF is also called GCD, or the greatest common divisor. The GCF of two numbers is the common factor between the numbers. When two co-primes are considered, the GCF will always be 1.

How to find the GCF of 8 and 12

To solve GCF, children learn different methods. A few well-known methods for solving GCF are as follows -

  1. Using Listing the Common Factors
  2. Using Prime Factorization
  3. Using Division Method

GCF of 8 and 12 Using Listing the Common Factors

Listing the factors of numbers is an easy method. We need to list all the factors of the numbers and find out the common factors between these numbers. Let’s find the GCF of 8 and 12 by listing the factors of both the numbers and then finding the common factor.

  • Factors of 8 are 1, 2, 4, and 8.
  • Factors of 12 are 1, 2, 3, 4, 6, and 12.

4 is the GCF of 8 and 12, as it is the largest common factor in both the factors list.

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GCF of 8 and 12 Using Prime Factorization

Prime factorization is the method of breaking down any number into its prime factors. The prime numbers that are common to both numbers will be multiplied together to get the GCF of the numbers.

Here, we find the GCF of 8 and 12 using prime factorization

Prime factorization of 8 = 2 × 2 × 2 = 23

Prime factorization of 12 = 2 × 2 × 3 = 22 × 31

GCF of 8 and 12 = 2 × 2 = 4.

GCF of 8 and 12 Using Division Method

The division method can be done by taking the large number as the dividend and the small number as the divisor. Take the remainder as the new divisor and make the previous divisor as the dividend. Divide it until the remainder becomes 0.

Division method to find the GCF of 8 and 12.


Step 1: Take the large number (12) as the dividend and the small number (8) as divisor.

Step 2: By dividing the numbers, 12 / 8, we get 4 as remainder and quotient as 1.

Step 3: Take the remainder (4) as the new divisor and the previous divisor (8) as the dividend.

Step 4: The division is continued further till the remainder is 0.

When the remainder is 0, we consider the last divisor as the GCF. Therefore, the GCF of 8 and 12 is 4.

Common Mistakes and How to Avoid Them in GCF of 8 and 12

While solving GCF, children make mistakes like considering the power of the same factor twice. Just to avoid these mistakes, few solutions are discussed below -

Problem 1

If one number is 8, and the GCF with another number, ‘b’ is 4 and the LCM of the two numbers is 24, find the other number.

Okay, lets begin

GCF x LCM = Product of the Numbers


4 x 24 = 8 x b


96 = 8 x b


b = 96 ÷ 8 = 12
 

Explanation

The equation GCF x LCM = Product of the Numbers, is taken and then solved to find the value of ‘b’. The value of b is 12.

Well explained 👍

Problem 2

If x is the GCF of 8 and 12 and solve 8x + 12x.

Okay, lets begin

GCF of 8 and 12


Factors of 8 = 1, 2, 4, and 8.


Factors of 12 = 1, 2, 3, 4, 6, and 12.


Therefore, GCF = 4

Substituting 4 into the equation, x = 4.


8x + 12x


= 8 x 4 + 12 x 4


= 32 + 48


= 80.

Explanation

The GCF of 8 and 12 is to be found, and the value is to be substituted into the equation 8x + 12x, the result will be 80.

Well explained 👍

Problem 3

Simplify the fraction of 8/12 using the GCF.

Okay, lets begin

The GCF of 8 and 12 is to be found.

     Prime factorization of 8 = 2 × 2 × 2 = 23


Prime factorization of 12 = 2 × 2 × 3 = 22 × 31

GCF of 8 and 12 = 2 x 2 = 4.

     Divide the numerator and denominator by 4


8/12 = 8 ÷ 4 / 12 ÷ 4

= 2/3

Explanation

The GCF of 8 and 12 is found by prime factorization. The fraction 8/12 is then divided by 4 on both numerator and denominator. The fraction will be ⅔.

Well explained 👍

Problem 4

Frank has 8 apples and 12 oranges. He wants to divide them into equal groups with no remainder. What is the largest number of groups he can form

Okay, lets begin

GCF of 8 and 12 is to be found


Factors of 8 = 1, 2, 4, and 8.


Factors of 12 = 1, 2, 3, 4, 6, and 12.


Therefore, GCF = 4

  Number of apples each group will have = 8 ÷ 4 = 2


Number of oranges each group will have = 12 ÷ 4 = 3.

Explanation

The GCF to be found of 8 and 12, is 4. The number of apples and oranges each group will have is found by dividing 8 and 12 by 4. Each group will have 2 apples and 3 oranges

Well explained 👍

Problem 5

A factory packs 8 containers in one box and 12 in another. What is the largest number of containers that can be repacked into boxes with the same number of containers in each, without mixing?

Okay, lets begin

The GCF of 8 and 12 is to be found


Factors of 8 = 1, 2, 4, and 8.


Factors of 12 = 1, 2, 3, 4, 6, and 12.


Therefore, GCF = 4

Thus, the number of containers that will be packed into each box will be 4.
 

Explanation

To find the number of containers that can be packed into each box without any mix up will be the GCF of 8 and 12. The GCF will be 4.

Well explained 👍

FAQs on Greatest Common Factor of 8 and 12

1.What is the product of GCF and LCM of 8 and 12?

The GCF of 8 and 12 is 4. The LCM of 8 and 12 is 24. The product of GCF and LCM is 96

2.Can 1 be GCF?

3.What is the HCF of 8 and 12?

4 is the HCF of 8 and 12.

4.Are GCF, HCF, and GCD the same?

Yes, GCF - Greatest Common Factor, HCF - Highest Common Factor and GCD - Greatest Common Divisor, all are of the same concept.

5.Can 0 be GCF?

Important Glossaries for GCF of 8 and 12

  • GCD: The Greatest Common Divisor or the largest number that is an integer and has the ability to divide two or more numbers. For example, GCF of 8 and 12 is 4.
  • Prime Factors: Prime factors of a number are the prime numbers that will be multiplied together to result in the original number.  For example, the prime factors of 12 are 2 × 2 × 3 = 12.
  • Co-prime Numbers: Two numbers are called co-prime numbers if 1 is their only common factor. For example, in 5 and 7, the only common factor is 1. 
  • Remainder: A remainder is the value that is left over after performing the division. For example, if 8 is divided by 5, we get 3 as remainder and 1 as quotient.
  • Dividend: The number that is getting divided by another number. For example, if 12 is divided by 5, 12 is the dividend.
  • Divisor: The number that divides the other number is called the divisor. For example, if 2 is divided by 5, 5 is the divisor

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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.