Question

If the highest power of 10. in N! be 16, find the highest
power of 10 in (N + 1)!​

Answer 1

Answer:

17

Step-by-step explanation:

10 = 2 * 5

in N!  the highest power of 10 = 16

Lets find Maximum possible values of n

There should be be 16 , 5s

5 , 10  , 15 , 20  , 25 (2 5s) , 30 , 35 , 40 , 45 , 50 (2 5s) , 55 , 60 , 65 , 70

= 16  (5s)  There are lot of 2 s

so 10 will have highest power = 16

N can be 70 to 74    as 75 will add another power of 10

if N = 70 the  (N + 1)! = 71! will have 16 as highest power of 10

if N = 71 the  (N + 1)! = 72! will have 16 as highest power of 10

if N = 72 the  (N + 1)! = 73! will have 16 as highest power of 10

if N = 73 the  (N + 1)! = 74! will have 16 as highest power of 10

if N = 74 the  (N + 1)! = 75! will have 17 as highest power of 10

=> the highest power of 10 in (N + 1)!​  = 17

Answer 2

Step-by-step explanation:

this may help you my friend.