Simplify the Fraction 16/36: Finding the Reduction Factor

Q: How do I find the greatest common factor?

List all factors of both numbers: 16: 1, 2, 4, 8, 16 and 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest number that appears in both lists is your GCF!

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

A factor is any number that divides evenly into another number. The simplification factor is specifically the GCF you use to reduce the fraction to its simplest form.

Q: Why can't I just divide by 2 like in the correct answer?

You can divide by 2, but that gives you $ \frac{8}{18} $, which isn't fully simplified! Always use the greatest common factor (4) to get $ \frac{4}{9} $ in one step.

Q: What if I get confused about which answer is correct?

Look carefully at the problem! The correct answer $ \frac{8}{18} $ with factor 2 matches dividing both parts by 2, but $ \frac{4}{9} $ would be the fully simplified form.

Fraction Simplification with Common Factors

Simplify the following fraction and specify the simplification factor:

$\frac{16}{36}$

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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 18

00:03 We'll reduce the fraction with the appropriate divisor so the denominator equals 18

00:08 Make sure to divide both numerator and denominator

00:13 Let's calculate the quotients

00:18 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 simplification 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 18.

Therefore:

$\frac{16:2}{36:2}=\frac{8}{18}$

Final Answer

$\frac{8}{18}$ , factor of 2

Key Points to Remember

Essential concepts to master this topic

Rule: Find the greatest common factor (GCF) of numerator and denominator
Technique: Divide both parts by GCF: 16÷4 = 4, 36÷4 = 9
Check: Verify no common factors remain in simplified fraction 4/9 ✓

Common Mistakes

Avoid these frequent errors

Using wrong common factor instead of GCF
Don't divide by 2 when GCF is 4 = partially simplified fraction 8/18! This leaves common factors remaining and isn't fully simplified. Always find the greatest common factor first.

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?

List all factors of both numbers: 16: 1, 2, 4, 8, 16 and 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest number that appears in both lists is your GCF!

What's the difference between a factor and the simplification factor?

A factor is any number that divides evenly into another number. The simplification factor is specifically the GCF you use to reduce the fraction to its simplest form.

Why can't I just divide by 2 like in the correct answer?

You can divide by 2, but that gives you $\frac{8}{18}$ , which isn't fully simplified! Always use the greatest common factor (4) to get $\frac{4}{9}$ in one step.

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. Check by listing factors or using the GCD method.

What if I get confused about which answer is correct?

Look carefully at the problem! The correct answer $\frac{8}{18}$ with factor 2 matches dividing both parts by 2, but $\frac{4}{9}$ would be the fully simplified form.

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