Question

if a(b!) is completely divisible by 5^11 where a is single digit number find the minimum value of b.​

Answer 1

Given :   a(b!) is completely divisible by 5^11 where a is single digit number

To find : the minimum value of b.​

Solution:

for minimum value of b

a = 5

5.b!  divisible by 5¹¹

=> b!  divisible by 5¹⁰

=> [b/5]  + [b/5²]  + [b/5³]  + ... + .   ≥  10  

b = 5

=> [5/5]  + [5/5²]  + [5/5³]  + ... + .  

= 1 + 0 +

= 1

b = 25

=> [25/5]  + [25/5²]  + [25/5³]  + ... + .  

= 5 + 1 + 0 + ..

= 6

b = 50

=> [50/5]  + [50/5²]  + [50/5³]  + ... + .  

= 10 + 2 + 0 + ..

= 12

b = 45

=> [45/5]  + [45/5²]  + [45/5³]  + ... + .  

= 9 + 1 + 0 + ..

= 10

Hence minimum value of b = 45

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Answer 2

refer the attached image for the answer

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