What is the largest value of n such that 10n divides the product 25 times 33 times 48 times 43 times...........

Quantitative Aptitude (CDS) Simplification

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What is the largest value of n such that 10ⁿ divides the product

2⁵ × 3³× 4⁸ × 4³ × 6⁷ × 7⁶ × 8¹² × 9⁹ × 10⁶ × 15¹² × 20¹⁴ × 22¹¹× 25¹⁵ ?

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Explanation:

For the number to be divisible by 10ⁿ, it must contain the same powers for 2 and 5
Power of 2 = 2^{5+2.8+7+3.12+6+2.14 + 11} = 2^{5+16+7+36+6+28+11} = 2109
Power of 5 = 5^{3+6+12+14+2.15} = 5⁶⁵
Hence maximum possible power of 10 can be 65 only.