# GCF of 12 and 20

Created by: Team Maths - Examples.com, Last Updated: May 27, 2024

## GCF of 12 and 20

To find the GCF (Greatest Common Factor) of 12 and 20, we start by listing the factors of each number. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 20 are 1, 2, 4, 5, 10, and 20. The common factors are 1, 2, and 4. The greatest of these common factors is 4. Therefore, the GCF of 12 and 20 is 4. This means that 4 is the largest numbers that can evenly divide both 12 and 20.

## Methods to Find GCF of 12 and 20

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

## GCF of 12 and 20 by Prime Factorization Method

Prime Factorization:

12: The prime factors of 12 are 2 and 3.

12 = 2 × 2 × 3

20: The prime factors of 20 are 2 and 5.

20 = 2 × 2 × 5

Identify Common Factors:

The common prime factors between 12 and 20 are 2 and 2.

Calculate the GCF:

Multiply the common prime factors together.

GCF = 2 × 2 = 4

Therefore, the GCF of 12 and 20 using the prime factorization method is 4.

## GCF of 12 and 20 by Long Division Method.

Divide the larger number by the smaller number:

Divide 20 by 12.

20 ÷ 12 = 1 remainder 8

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

Now, divide 12 by the remainder 8.

12 ÷ 8 = 1 remainder 4

Continue the process:

Next, divide 8 by the remainder 4.

8 ÷ 4 = 2 remainder 0

Identify the GCF:

Since the remainder is now 0, the divisor at this step is the GCF.

Therefore, the GCF of 12 and 20 using the long division method is 4.

## GCF of 12 and 20 by Listing Common Factors

List the factors of each number:

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

Factors of 20: 1, 2, 4, 5, 10, 20

Identify the common factors:

Common factors of 12 and 20: 1, 2, 4

Determine the greatest common factor:

The largest common factor is 4.

Therefore, the GCF of 12 and 20 by listing common factors is 4.

## What is the common multiple of 12 and 20?

The common multiples of 12 and 20 are numbers that both 12 and 20 can divide without leaving a remainder. The smallest common multiple is 60, known as the least common multiple (LCM).

## What is the greatest common factor of 12 and 20 brainly?

The greatest common factor (GCF) of 12 and 20 is 4. This is the largest number that divides both 12 and 20 without leaving a remainder.

## Why is 4 the GCF of 12 and 20?

4 is the largest number that can evenly divide both 12 and 20.

## Can the GCF of 12 and 20 be greater than 12?

No, the GCF is always less than or equal to the smaller number, which is 12.

## How does finding the GCF help in simplifying fractions?

The GCF is used to simplify fractions by dividing the numerator and the denominator by the GCF.

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