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Quantitative Aptitude

Highest Power of a Number

If 146 ! is d...

Question

If 146! is divided by $6^{k}$ then find the maximum value of k.___

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Solution

We need to find the highest power of 6 contained in 146!
Now, $6 = 2 \times 3$ . As 3 is the largest prime factor of 6, we'll find the highest power of 3 in 146!
The highest power of 3 in 146! = 48 + 16 + 5 + 1 = 70
Hence, k = 70

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