518:74

To simplify the fraction \( \frac{518}{74} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD).

1. Find the GCD of 518 and 74.

   • The prime factorization of 74 is \( 2 \times 37 \).
   • The number 518 can be divided by 2 because it is even: \( 518 \div 2 = 259 \).
   • The number 259 can be divided by 7 but is not divisible by 2 or 37, meaning 74 is not a factor of 518.
   • Thus, the GCD is 2.

2. Divide both the numerator and the denominator by 2: \[ \frac{518 \div 2}{74 \div 2} = \frac{259}{37} \]

3. Now, check if this fraction can be simplified further:

   • 259 is \( 7 \times 37 \), hence \( 37 \) is a common factor.

4. Thus, simplifying further: \[ \frac{259 \div 37}{37 \div 37} = \frac{7}{1} = 7 \]

So, \( \frac{518}{74} = 7 \).