84000:1610

The ratio 84000:1610 can be simplified. To do this, we need to divide both sides of the ratio by their greatest common divisor (GCD).

First, let's find the GCD of 84000 and 1610.

1. The prime factorization of 84000:

   • 84000 = 84 × 1000 = 84 × (10^3) = 84 × (2^3 × 5^3)
   • 84 = 2^2 × 3 × 7
   • Hence, 84000 = 2^5 × 3^1 × 5^3 × 7^1

2. The prime factorization of 1610:

   • 1610 = 161 × 10 = 161 × (2 × 5)
   • 161 = 7 × 23
   • Hence, 1610 = 2^1 × 5^1 × 7^1 × 23^1

Now, identify the common prime factors:

• Both 84000 and 1610 have the factors 2, 5, and 7.

3. The GCD is:

   • 2^1 × 5^1 × 7^1 = 70

4. Now divide both components of the ratio by the GCD:

   • 84000 ÷ 70 = 1200
   • 1610 ÷ 70 = 23

Thus, the simplified ratio is 1200:23.