Question

Simplify 75/105

Answer 1

To simplify the fraction \( \frac{75}{105} \), we first find the greatest common divisor (GCD) of the numerator and denominator.

1. **Factors of 75**:
- 75 can be factored into \( 3 \times 5^2 \) or \( 3 \times 15 \).

2. **Factors of 105**:
- 105 can be factored into \( 3 \times 5 \times 7 \).

3. **Common factors**:
- The common factors of 75 and 105 are 3 and 5.

4. **GCD**:
- The GCD is \( 3 \times 5 = 15 \).

Now we can simplify the fraction by dividing both the numerator and the denominator by their GCD:

\[
\frac{75 \div 15}{105 \div 15} = \frac{5}{7}
\]

Thus, the simplified form of \( \frac{75}{105} \) is \( \frac{5}{7} \).