345 : 4668

To simplify the ratio \( 345 : 4668 \), you can divide both numbers by their greatest common divisor (GCD).

1. First, find the GCD of 345 and 4668.
   • The prime factors of 345 are \( 3 \times 5 \times 23 \).
   • The prime factors of 4668 are \( 2 \times 3 \times 389 \).

The GCD is 3 (the only common factor).

2. Now, divide both numbers by 3:

   • \( 345 \div 3 = 115 \)
   • \( 4668 \div 3 = 1556 \)

Thus, the simplified ratio \( 345 : 4668 \) is \( 115 : 1556 \).

You can check if this can be simplified further, but there are no common factors between 115 and 1556, so \( 115 : 1556 \) is in its simplest form.