The power of 2 in 400! is 397.
What is the method of determination of power of prime in Factorial ?
Let p is the prime number whose power is to be found
Let n is the factorial number then
p in n! = (n /p) + (n/p²) +(n/p³) + .......
until Numerator < Denominator
and after division only the integer part is taken
Therefore to determine the power of 2 in 400!
2 in 400! = (400 /2) + ( 400 /2²) + (400 /2³) +(400 /2⁴) +(400 /2⁵) +(400 /2⁶) +(400 /2⁷) +(400 /2⁸) + above this N < D
2 in 400! = 200 +100 +50+25+12+6+3+1
2 in 400 = 397
Therefore the power of 2 in 400! is 397.
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