Greatest Common Factor of 18 and 12

Grade 6 Math Worksheets

The greatest common factor (GCF), also known as the greatest common divisor (GCD) or the highest common factor (HCF), of 18 and 12 is the largest positive integer that divides both of these numbers evenly.

To find the GCF of 18 and 12, you can determine the common factors of both numbers and then select the greatest one.

In this article, we will cover:

Methods to find GCF of 18 and 12
Prime Factorisation
Long Division method
Listing common factors
Solved Examples
FAQs

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Greatest Common Factor of 18 and 12 - Grade 6 Math Worksheet PDF

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Methods to find GCF of 18 and 12

You can use a few methods to find the greatest common factor (GCF) of 18 and 12.

Prime Factorisation
Long Division method
Listing common factors

Prime Factorization Method:

Find the prime factorization of each number.
For 18: 18 = 2 x 3 x 3
For 12: 12 = 2 x 2 x 3
Identify and multiply the common prime factors and multiply them: 2 x 3 = 6.
Hence, the GCF of 18 and 12 is 6.

Long Division Method:

This method involves successive division and finding remainders.
Divide the larger number (18) by the smaller number (12): 18 ÷ 12 = 1 with a remainder of 6.
Now, divide the smaller number (12) by the remainder (6): 12 ÷ 6 = 2 with no remainder.
Continue this process until you get a remainder of 0. The divisor at this step is the GCF, which is 6.

Listing Common Factors

List the factors of both numbers and then identify the common factors.

Factors of 18: 1, 2, 3, 6, 9, 18

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

Common factors: 1, 2, 3, and 6

Among these common factors, the greatest one is 6.

Therefore, the greatest common factor of 18 and 12 is 6.

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Solved Examples

1. What is the GCF of 18 and 12 if the LCM is 36?

If the least common multiple (LCM) of 18 and 12 is 36, you can use the relationship between the GCF and LCM to determine the GCF.

The relationship is GCF × LCM = Product of the two numbers.

In this case, the product of 18 and 12 is 216 (18 × 12), and the LCM is 36.

So, GCF × 36 = 216

GCF = 216 / 36

GCF = 6

2. The greatest common factor (GCF) is 5 for two numbers, and the least common multiple (LCM) is 60. If one of the numbers is 15, what is the other number?

Given: Greatest Common Factor (GCF) = 5 , Least Common Multiple (LCM) = 60 One number = 15

Let the other number be “x”.

We know that GCF × LCM = Product of the two numbers.

So, 5 × 60 = 15 × x.

Solving for x: 300 = 15x

x = 300 / 15

x = 20

Therefore, the other number is 20.

3. Show the relation between GCF and LCM of 18 and 12.

The relation between GCF and LCM of 18 and 12 is

GCF × LCM = Product of the two numbers.

For the numbers 18 and 12:

GCF of 18 and 12 = 6

LCM of 18 and 12 = 36

Now, let’s verify the relationship:

GCF × LCM = Product of the two numbers

6 × 36 = 18 × 12

216 = 216

As you can see, the product of the GCF and the LCM is indeed equal to the product of the two numbers, which confirms the relationship.

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FAQs

What is the GCF of 18 and 12?

The GCF (Greatest Common Factor) of 18 and 12 is 6.

How do you find the GCF of 18 and 12?

To find the GCF of 18 and 12, you can use various methods, including prime factorization, listing factors, or the method of finding the greatest common divisor (GCD).

What are the factors of 18 and 12?

The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12.

Why is 6 the GCF of 18 and 12?

The GCF is the largest number that divides both 18 and 12 evenly. In this case, 6 is the largest number that is a common factor of both 18 and 12.

Can you find the GCF using prime factorization?

Yes, you can find the GCF of 18 and 12 using prime factorization. First, express both numbers as a product of their prime factors. Then, the GCF is the product of the common prime factors with their lowest powers.

What is the relationship between GCF and LCM?

The GCF (Greatest Common Factor) and the LCM (Least Common Multiple) are related by the formula: GCD(a, b) * LCM(a, b) = a * b. In this case, for 18 and 12, GCF(18, 12) * LCM(18, 12) = 6 * 36 = 18 * 12 = 216.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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