To simplify the fraction \( \frac{75}{105} \), we first find the greatest common divisor (GCD) of the numerator and denominator.
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Factors of 75:
- 75 can be factored into \( 3 \times 5^2 \) or \( 3 \times 15 \).
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Factors of 105:
- 105 can be factored into \( 3 \times 5 \times 7 \).
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Common factors:
- The common factors of 75 and 105 are 3 and 5.
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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 \( \frac{5}{7} \).