Simplify the Fraction 20/50: Finding the Highest Common Factor

Q: How do I find the greatest common factor of 20 and 50?

List the factors of each number: 20: 1, 2, 4, 5, 10, 20 and 50: 1, 2, 5, 10, 25, 50. The largest number that appears in both lists is 10, so that's your GCF!

Q: What if I divided by 5 instead of 10?

You'd get $ \frac{4}{10} $, which isn't fully simplified! You can still divide both 4 and 10 by 2 to get $ \frac{2}{5} $. Always check if your answer can be simplified further.

Q: Why is 10 the greatest common factor and not 5?

Both 20 and 50 are divisible by 10: 20 ÷ 10 = 2 and 50 ÷ 10 = 5. Since 10 is larger than 5 and divides both numbers, it's the greatest common factor.

Fraction Simplification with Greatest Common Factor

Simplify the fraction below and specify the highest common factor:

$\frac{20}{50}$

❤️ 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 Reduce the fraction to denominator 5

00:03 We'll reduce the fraction with the appropriate divisor so the denominator equals 5

00:06 Make sure to divide both numerator and denominator

00:10 Calculate the quotients

00:16 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:

$\frac{20}{50}$

Step-by-step solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 50, gives us a result of 5:

$\frac{20:10}{50:10}=\frac{2}{5}$

Final Answer

$\frac{2}{5}$ , 10

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor of numerator and denominator
Technique: Divide both 20 and 50 by their GCF of 10
Check: Verify $\frac{2}{5}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Using the wrong common factor
Don't divide by any common factor like 2 or 5 = partially simplified fraction! This gives answers like $\frac{10}{25}$ or $\frac{4}{10}$ which aren't fully simplified. Always find the greatest common factor to get the simplest form.

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 greatest common factor of 20 and 50?

List the factors of each number: 20: 1, 2, 4, 5, 10, 20 and 50: 1, 2, 5, 10, 25, 50. The largest number that appears in both lists is 10, so that's your GCF!

What if I divided by 5 instead of 10?

You'd get $\frac{4}{10}$ , which isn't fully simplified! You can still divide both 4 and 10 by 2 to get $\frac{2}{5}$ . Always check if your answer can be simplified further.

Why is 10 the greatest common factor and not 5?

Both 20 and 50 are divisible by 10: 20 ÷ 10 = 2 and 50 ÷ 10 = 5. Since 10 is larger than 5 and divides both numbers, it's the greatest common factor.

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 $\frac{2}{5}$ , the only common factor of 2 and 5 is 1, so it's fully simplified!

What's the difference between any common factor and the greatest common factor?

Using any common factor will simplify the fraction, but only the greatest common factor will give you the most simplified form in one step. It's more efficient and ensures you get the final answer!

🌟 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