exact power of 5

87! is 1 * 2 *....5......10.....25.......50........75......80 .....85*86*87
5¹ will divide each of 5 , 10 for 10 we need 2 so till 85 we need 17 so 5 to the power 17
but 5² is needed to divide 25,50, 75 all multiple of 25
i.e. another 5³
IMO D

sanju09 wrote:What exact power of 5 divides 87! (read factorial 87)?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 23

a short cut :

the power will be :

Sum of quotients of division of 87 by powers of 5 ( you need to take all the powers which are less than or equal to 87) :

hence, in our case :

87/5+87/(5^2) ---------- you can't take third power of 5 because it is greater than 87.

therefore, answer = 17 + 3 = 20

harshavardhanc wrote:

sanju09 wrote:What exact power of 5 divides 87! (read factorial 87)?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 23

a short cut :

the power will be :

Sum of quotients of division of 87 by powers of 5 ( you need to take all the powers which are less than or equal to 87) :

hence, in our case :

87/5+87/(5^2) ---------- you can't take third power of 5 because it is greater than 87.

therefore, answer = 17 + 3 = 20

That's perfect!