Question

Find greatest number of 4 digit which is divisble by 8 and 11 both

Answer 1

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3 ANSWERS

Shubham Patil, Assistant System Engineer at Tata Consultancy Services (2016-present)
Answered May 4, 2018 · Author has 242 answers and 10.7k answer views
Method 1:

Find LCM of 8 and 11

As both are coprime numbers

LCM (8,11)=8×11=88

Therefore number will be multiple of 88.

Largest 4 digit number is 9999 and is not divisible by 8 and 11

Therefore expected number will be less than 9999

100th multiple of 88=88×100=8800.

110th multiple of 88=88×110=9680

111th multiple of 88=88×111=9768

113th multiple of 88=88×113=9944

114th multiple of 88=88×114=10032

Above all 5 numbers are divisible by 8 and 11

But largest 4 digit number from above 5 is 9944

Answer is 9944

Method 2:

Divisibility rule of 8= Last three digits of number should be divisible by 8

Divisibility rule of 11=Difference between sum of odd digits and even digits of number should be 0 or divisible by 11.

Now, largest 4 digit number is 9999

If 9999 divided by 8 gives remainder 7

Therefore largest 4 digit number divisible by 8 is 9999–7=9992

But it is not divisible by 11

Now we will check numbers less than 9992 which are divisible by 11

They are 9988,9977,9966,9955,9944,9933..

Among above numbers we have to check which number is divisible by 8

Only 9994 is divisible by 8 as it's last 3 digits are divisible by 8.

Therefore the number is 9944

Answer 2

lcm of 8 and 11 is 88
divide 9999 by 88
remainder= 55
9999-55= 9944