Find maximum power of 2 by which factorial 100 (100!) is divisible !
Asked by an IIT JEE ASPIRANT
Answers
Hey there!
To find maximum power on any number 'n' by which factorial 'f!' is divisible, We follow some steps. They are discussed below.
• Factorise the number 'n' into primes.
• Now find highest power of all prime number in that factorial 'f!'. To do so divide 'f' continuously by 'n' and get the sum of all the quotients.
• And write down the least power. It will be your answer.
Now coming to the question,
We have to find maximum power of 2 by which 100! is divisible.
So, following above steps we can do it easily. 2 is smallest prime so we need not to factor it.You don't have the need to take decimal values. Let's do it now.
100 / 2 = 50
50 / 2 = 25
25 / 2 = 12
12 / 2 = 6
6 / 2 = 3
3 / 2 = 1
Sum of all the quotients = (50 + 25 + 12 + 6 + 3 + 1) = 97
Hence, the maximum power of 2 by which factorial 100! is divisible is 97.
Answer:
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