Question

Find the maximum power of 8 in 100!​

Answer 1

Given :   100!​

To Find : maximum power of 8 in 100!​

Solution:

8  = 2³

maximum power of 2  in 100!​

= [100/2]  + [100/2²]  + [100/2³] + [100/2⁴]  + [100/2⁵] + [100/2⁶]  + [100/2⁷] + .. + ...+ ..  +

= 50  + 25  + 12 + 6 + 3 + 1 + 0 + ..

= 97

= 3 * 32 + 1

2⁹⁷ = (2³)³².2 =   2. 8³²

Hence maximum power of 8 can be 32  

maximum power of 8 in 100!​  = 32

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