Question

Find the maximum value of n such that 210! is perfectly divisible by 15n?
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Answer 1

Step-by-step explanation:

52/3 = 17

17/3 = 5

5/3 = 1

1 is the answer

Answer 2

Given :   210! is perfectly divisible by 15ⁿ

To Find : maximum value of n

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Solution:

210! is perfectly divisible by 15ⁿ

15ⁿ = 3ⁿ * 5ⁿ

5 will have less numbers than 3 hence checking for 5

[210 /5]  + [210 / 5²]  + [210/ 5³ ] +  [210/ 5⁴ ] + ____

= 42 +  8  + 1 + 0  + 0 ___

51

Hence maximum possible value of n is 51

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