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

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 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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