Simplify 24/36

Reduce the fraction 24/36 to its lowest terms with a complete step-by-step solution.

Answer: 24/36 = \frac{2}{3}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 24/36 to its lowest terms.

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1.

\frac{24}{36} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 24 (the numerator).

Factors are numbers that divide evenly into 24.

\text{Factors of } 24: 1, 2, 3, 4, 6, 8, 12, 24

Step 3 Find Factors of the Denominator

Now let's find all factors of 36 (the denominator).

\text{Factors of } 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 24 and 36 are: 1, 2, 3, 4, 6, 12

The Greatest Common Factor (GCF) is the largest of these: 12

We will divide both the numerator and denominator by 12.

\text{GCF}(24, 36) = 12

Step 5 Divide Both by the GCF

Divide the numerator by 12: 24 ÷ 12 = 2

Divide the denominator by 12: 36 ÷ 12 = 3

\frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}

Step 6 Final Answer

The simplified fraction is 2/3

We can verify: 2 × 12 = 24 and 3 × 12 = 36 ✓

2 and 3 have no common factors, so this is fully simplified.

\frac{24}{36} = \frac{2}{3}