Question

Find maximum power of 2 by which factorial 100 (100!) is divisible !

Asked by an IIT JEE ASPIRANT ​

Answer 1

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 2

Answer:

me sorry to you actually miss understanding ho gyi

me also in class 10 and an IIT ASPIRANT

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