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.

GCF of 12 and 20

GCF of 12 and 20 is 4.

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.