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.

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

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.

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.

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.

• 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