3663:252

To simplify the ratio 3663:252, we need to divide both numbers by their greatest common divisor (GCD).

1. First, we'll find the GCD of 3663 and 252.

2. The prime factorization of 3663 is:

   • 3663 = 3 × 1221
   • 1221 = 3 × 407
   • 407 = 11 × 37
   • Therefore, 3663 = \(3^2 \times 11 \times 37\).

3. The prime factorization of 252 is:

   • 252 = 2 × 126
   • 126 = 2 × 63
   • 63 = 3 × 21
   • 21 = 3 × 7
   • Therefore, 252 = \(2^2 \times 3^2 \times 7\).

4. The GCD of 3663 and 252 will involve the lowest powers of common prime factors:

   • The common factor is 3 with the lowest power being \(3^2\).
   • Thus, GCD(3663, 252) = \(3^2 = 9\).

5. Now, we simplify the ratio:

   • Divide both numbers by the GCD (9):
   • \(3663 ÷ 9 = 407\)
   • \(252 ÷ 9 = 28\)

Therefore, the simplified ratio of 3663:252 is 407:28.