What is equivalent to 1800:375

Question

ScanSolve AI Tutor · Accepted Answer

This is a ratio problem. To find the equivalent ratio, we need to simplify the given ratio by dividing both numbers by their greatest common divisor (GCD).

Find the GCD of 1800 and 375.
We can use prime factorization or the Euclidean algorithm.
Prime factorization of 1800: 1800 = 18 × 100 = (2 × 3²) × (10²) = (2 × 3²) × (2 × 5)² = 2 × 3² × 2² × 5² = 2³ × 3² × 5²
Prime factorization of 375: 375 = 5 × 75 = 5 × (3 × 25) = 5 × 3 × 5² = 3 × 5³
The common prime factors are 3 and 5. The lowest power of 3 is 3¹ and the lowest power of 5 is 5².
GCD(1800, 375) = 3¹ × 5² = 3 × 25 = 75.
Divide both numbers in the ratio by the GCD.
1800 ÷ 75 = 24
375 ÷ 75 = 5

The equivalent ratio is 24:5.

What is equivalent to 1800:375

Step-by-step solution

Find the GCD of 1800 and 375.

Divide both numbers in the ratio by the GCD.

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