Express 24:36 in its simplest form.

Answer

To express the ratio 24:36 in its simplest form, we can follow these steps:

### Step 1: Write the ratio as a fraction
We start by expressing the ratio 24:36 as a fraction:
\[ \frac{24}{36} \]

### Step 2: Find the greatest common divisor (GCD)
Next, we need to find the greatest common divisor (GCD) of the two numbers, 24 and 36. The GCD is the largest number that divides both numbers without leaving a remainder.

- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are: 1, 2, 3, 4, 6, 12. The greatest of these is 12.

### Step 3: Divide both numbers by the GCD
Now, we divide both the numerator and the denominator by the GCD (which is 12):
\[ \frac{24 \div 12}{36 \div 12} = \frac{2}{3} \]

### Step 4: Write the simplified ratio
Now, we can express the simplified fraction back as a ratio:
\[ 2:3 \]

Thus, the simplest form of the ratio 24:36 is:
\[ \boxed{2:3} \]

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