Question

The number of digits in the smallest positive integer which is composed entirely of fives that is divisible by 99 is

Answer 1

Hello ,

Answer: Number of digits in that number is 18

The number which entirely composed of 5 only is

555,555,555,555,555,555

that is divided by 99 completely.

On dividing 555,555,555,555,555,555/99 = 5,611,672,278,338,945

I don't implies any logic,because don't recall any such logic.So,I just did hit and trial.

Hope it helps you.

Answer 2

Answer:

Eighteen's (18) times five is the smallest number which completely divide by 99. {5,55,55,55,55,55,55,55,555}

Step-by-step explanation:

Hey Mate,

I will tell you the simple logic to find out the answer of this type of question.

Before that i will provide you some information about divisibility rules,

So,

The Divisibility Rule of 99 : If the number is divide by 11 and 9 both then that number is also divided by 99.

The Divisibility Rule of 9 : If sum of all digit of number is divided by 9 then the whole number is divided by 9.

The Divisibility Rule of 11 : If the sum of alternate digit is subtract from another sum of alternate digit and if answer is -11 ,11, 0r 0 then the whole number is divide by 11.

So, we need to find out the combination of number which divide by 11 and 9 both so its automatically divided by 99.

So, If we take 5 two times then => 55

55 (Check Divisibility Rule of 11 =  +5-5 = 0 ,  So, if take 2,4,6,8,10... (Multiple of 2) times of 5 so its completely divide by 11)

55 (Check Divisibility Rule of 9 = 5+5 = 10 and 10 is not divide by 9. so find out another number in same series. So, if first number 10 so second is 20 then 30, 40, 50, ......,90 .& 90 is completely divided by 9 )

So, Sum of all digit is 90 we we take 5 eighteen's (18) times. And 18 is also the multiple of 2.

So,

Eighteen's (18) times five is the smallest number which completely divide by 99. {5,55,55,55,55,55,55,55,555}