## GCF of 8 and 12

To find the Greatest Common Factor (GCF) of 8 and 12, use one of three methods: prime factorization, long division, or listing common factors. By prime factorization, 8 is 2³ and 12 is 2²× 3 , with the common factor being 2², which is 4. Using the long division method, dividing 12 by 8 gives a remainder of 4, and dividing 8 by 4 leaves a remainder of 0, making 4 the GCF. Listing factors, 8’s factors are 1, 2, 4, 8, and 12’s factors are 1, 2, 3, 4, 6, 12; the greatest common factor is 4. Thus, the GCF of 8 and 12 is 4.

## GCF of 8 and 12

### GCF of 8 and 12 is 4.

The GCF of 8 and 12 is 4, found by prime factorization (common factor 2²), long division (remainder zero at 4), or listing common factors (1, 2, 4).

## Methods to Find GCF of 8 and 12

- Prime Factorization Method
- Long Division Method
- Listing Common Factors

## GCF of 8 and 12 by Prime Factorization Method

**Prime factorize each number:**

**Prime factors of 8:**8 = 2 × 2 × 2³**Prime factors of 12:**12 = 2 × 2 × 3 =2²×3

**Identify the common prime factors:**

- The common prime factor is 2.
- The smallest power of the common factor 2 in both factorizations is 2².

**Multiply the common prime factors with the smallest exponents:**

**GCF = **2² = 4

## GCF of 8 and 12 by Long Division Method.

**Divide the larger number by the smaller number:**

- Larger number: 12
- Smaller number: 8

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

**Replace the larger number with the smaller number and the smaller number with the remainder:**

- New larger number: 8
- New smaller number: 4

**Divide the new larger number by the new smaller number:**

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

**Repeat the process until the remainder is 0:**

- In the second step, the remainder is 0, which means the process stops here.

**The divisor at this step is the GCF:**

The divisors at the last step before the remainder became 0 is 4.

## GCF of 8 and 12 by Listing Common Factors

**List the factors of each number:**

**Factors of 8:** 1, 2, 4, 8

**Factors of 12:** 1, 2, 3, 4, 6, 12

**Identify the common factors:**

The common factors of 8 and 12 are: 1, 2, 4

**Determine the greatest common factor:**

Among the common factors, the largest one is 4.

## What is the GCF of 8 and 12?

The Greatest Common Factor (GCF) of 8 and 12 is 4.

## Can the GCF be larger than the smallest number?

No, the GCF cannot be larger than the smallest of the given numbers.

## What is the relationship between GCF and LCM?

The product of the GCF and the Least Common Multiple (LCM) of two numbers equals the product of the numbers themselves.

## How can understanding GCF benefit students in math?

Understanding GCF helps students simplify fractions, solve problems involving divisors, and enhance their number theory skills.

## What is the GCF of 8 and 12 used for in real life?

The GCF can be used for reducing fractions, dividing items into equal groups, and solving problems in finance, engineering, and computer science.

## Can the GCF of two numbers be one of the numbers?

Yes, if one number is a multiple of the other, the GCF is the smaller number. For example, the GCF of 4 and 8 is 4.