Simplify the Fraction 18/36: Finding the Highest Common Factor

Q: How do I find the highest common factor of 18 and 36?

List the factors of each number: 18: 1, 2, 3, 6, 9, 18 and 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest number that appears in both lists is 18.

Q: What's the difference between a common factor and the highest common factor?

A common factor divides both numbers evenly (like 1, 2, 3, 6, 9, 18 for this problem). The highest common factor (HCF) is the largest of these, which is 18.

Q: Can I use prime factorization to find the HCF?

Yes! Write 18 = 2 × 3² and 36 = 2² × 3². The HCF uses the lowest power of each common prime: 2¹ × 3² = 18.

Q: How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator have no common factors except 1. For example, 6/12 can still be divided by 6 to get 1/2.

Fraction Simplification with Highest Common Factor

Simplify the fraction below and specify the highest common factor:

$\frac{18}{36}=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction to denominator 12

00:03 Let's reduce the fraction with the appropriate divisor so the denominator equals 12

00:06 Make sure to divide both numerator and denominator

00:10 Let's calculate the quotients

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the fraction below and specify the highest common factor:

$\frac{18}{36}=\text{ ?}$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 36, gives us a result of 12.

Therefore:

$\frac{18:3}{36:3}=\frac{6}{12}$

Final Answer

$\frac{6}{12}$ , 3

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 18 and 36 by their GCF of 18
Check: Verify $\frac{6}{12}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the highest common factor
Don't divide 18/36 by 3 to get 6/12 and stop there = incomplete simplification! This leaves the fraction not fully reduced. Always find the highest common factor (18) to get the simplest form 1/2.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

$\frac{4}{8}=$

FAQ

Everything you need to know about this question

How do I find the highest common factor of 18 and 36?

List the factors of each number: 18: 1, 2, 3, 6, 9, 18 and 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest number that appears in both lists is 18.

Why is the answer 6/12 and not 1/2?

The question asks you to divide by a specific factor that results in a denominator of 12. So we divide by 3 (not 18) to get $\frac{6}{12}$ , even though this isn't fully simplified.

What's the difference between a common factor and the highest common factor?

A common factor divides both numbers evenly (like 1, 2, 3, 6, 9, 18 for this problem). The highest common factor (HCF) is the largest of these, which is 18.

Can I use prime factorization to find the HCF?

Yes! Write 18 = 2 × 3² and 36 = 2² × 3². The HCF uses the lowest power of each common prime: 2¹ × 3² = 18.

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator have no common factors except 1. For example, 6/12 can still be divided by 6 to get 1/2.

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