Determine the number of trailing zeros in the product of

Solution

Total number of 5’s in the given expression: 5⁵ = 1⁵ × 5⁵ = 5 10¹⁰ = 2¹⁰ × 5¹⁰ = 10 15¹⁵ = 3¹⁵ × 5¹⁵ = 15 20²⁰ = 4²⁰ × 5²⁰ = 20 Total number of 2’s in the given expression: 2² = 2 4⁴ = (2²)⁴ = 2⁸ = 8 6⁶ = (2 × 3)⁶ = 2⁶ × 3⁶ = 6 8⁸ = (2³)⁸ = 2²⁴ = 24 10¹⁰ = 2¹⁰ × 5¹⁰ = 10 So, total number of 5’s in the given expression = 5 + 10 + 15 + 20 = 50 And, at least 50 2’s in the given expression So, number of zeroes at the end of the product = 50