Simplify the Fraction 16/36 and Find Its Highest Common Factor

Q: How do I find the GCF of 16 and 36?

List the factors of each number: 16: 1, 2, 4, 8, 16 and 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest number that appears in both lists is 4!

Q: Why can't I just divide by 2 since both numbers are even?

You could, but then you'd get $ \frac{8}{18} $ which still isn't simplified! You'd need to divide by 2 again. It's faster to find the GCF (4) and do it in one step.

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

A fraction is fully simplified when the numerator and denominator share no common factors except 1. For $ \frac{4}{9} $, the only common factor is 1, so it's done!

Q: Is the GCF always the same as the number I divide by?

Yes! The GCF is exactly the number you divide both the numerator and denominator by to get the simplified fraction. In this problem, GCF = 4.

Fraction Simplification with Greatest Common Factor

Simplify the following fraction and specify the highest common factor:

$\frac{16}{36}=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduced the fraction to denominator - 4

00:03 Divide the fraction by the appropriate factor

00:06 Make sure to divide both numerator and denominator

00:11 Calculate the quotients

00:17 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 following fraction and specify the highest common factor:

$\frac{16}{36}=$

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 9.

Therefore:

$\frac{16:4}{36:4}=\frac{4}{9}$

Final Answer

$\frac{4}{9}$ , 4

Key Points to Remember

Essential concepts to master this topic

Rule: Find the GCF of numerator and denominator first
Technique: Divide both parts by GCF: $\frac{16÷4}{36÷4}=\frac{4}{9}$
Check: Verify 4 and 9 share no common factors except 1 ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the greatest one
Don't divide 16/36 by 2 to get 8/18 and stop there = fraction not fully simplified! You need to keep going until no common factors remain. Always find the Greatest Common Factor (GCF = 4) and divide both parts by it in one step.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I find the GCF of 16 and 36?

List the factors of each number: 16: 1, 2, 4, 8, 16 and 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest number that appears in both lists is 4!

Why can't I just divide by 2 since both numbers are even?

You could, but then you'd get $\frac{8}{18}$ which still isn't simplified! You'd need to divide by 2 again. It's faster to find the GCF (4) and do it in one step.

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator share no common factors except 1. For $\frac{4}{9}$ , the only common factor is 1, so it's done!

What if I can't find any common factors?

If the numerator and denominator share no common factors except 1, the fraction is already in its simplest form! The GCF would be 1 in this case.

Is the GCF always the same as the number I divide by?

Yes! The GCF is exactly the number you divide both the numerator and denominator by to get the simplified fraction. In this problem, GCF = 4.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime