Reduce `45/105` in its irreducible form.

Answer

To reduce the fraction \( \frac{45}{105} \) to its irreducible form, we will follow these steps:

### Step 1: Find the Greatest Common Divisor (GCD)
To simplify the fraction, we first need to find the GCD of the numerator (45) and the denominator (105).

- **Factors of 45**:
- 1, 3, 5, 9, 15, 45
- **Factors of 105**:
- 1, 3, 5, 7, 15, 21, 35, 105

The common factors are 1, 3, 5, and 15. The greatest of these is 15.

### Step 2: Divide Both Numerator and Denominator by the GCD
Now, we will divide both the numerator and the denominator by the GCD (15).

\[ \frac{45 \div 15}{105 \div 15} = \frac{3}{7} \]

### Step 3: Check if the Resulting Fraction is in Irreducible Form
Now we need to check if \( \frac{3}{7} \) can be simplified further. The factors of 3 are 1 and 3, and the factors of 7 are 1 and 7. Since they have no common factors other than 1, \( \frac{3}{7} \) is indeed in its irreducible form.

### Final Answer
Thus, the irreducible form of \( \frac{45}{105} \) is \( \frac{3}{7} \).

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