Find the highest common factor (H.C.F) of the following numbers: 4 × 27 × 3125, 8 × 9 × 25 × 7, and 16 × 81 × 5 × 11 × 49.

Explanation

First, express each number as a product of prime factors: 4 × 27 × 3125 = 2² × 3³ × 5⁵; 8 × 9 × 25 × 7 = 2³ × 3² × 5² × 7; 16 × 81 × 5 × 11 × 49 = 2⁴ × 3⁴ × 5 × 7² × 11. The H.C.F is the product of the lowest powers of common primes: 2² × 3² × 5 = 180.