Question

What is the largest power of 2 that divides 200!/100! . (with complete solution)

Answer 1

200! / 100! will be divisible by no. 128 that is
${2}^{7}$

It is so because after division of 200!/100!

Number remaining in multiply are from 101 to 200.

101*102*103*..............*199*200

And in all these 2 raised to the power 7 that is 128 comes which means 128 divide the series.

So largest power of 2 that divides 200!/100 is 7.

Thank you.

Answer 2

Largest power of 2 in 200! by Legendre's formula :

100 + 50 + 25 + 12 + 6 + 3 + 1 = 197

Similarly, largest power of  2 in 100! is :

= = 50 + 25 + 12 + 6 + 3 + 1 = 97

Thus, Largest power of 2 in ​ is = 197−97 = 100

HOPE IT HELPS ...