What will be the value of x for
(100^17 –1)+(10^34 + x)÷9
; the remainder = 0
Answers
Step-by-step explanation:
As 10 power any number minus 1 is multiple of 9(e.g 9,99,999…),10 power 17 minus 1 is also a multiple of 9.let 10 power 34 +x be K . When we add 10 power 17 with K and then divide by 9, the remainder is 0 hence that number is perfectly divisible by 9. 10 power 17 minus 1 is already divisible by nine. If we add another multiple of nine, only then will the remainder be 0. Hence K is a multiple of 9. All multiples have sum of their digits as 9 or a whole number multiple of 9. Hence 10 power 34+ X should have its sum of digits as multiple of 9. Now if X is 8 , 10 power 34 plus x which we named K will be something like this 1000……008.
Hence least natural number value of X is 8. X can be generalised as 8 + 9n where n is an integer. So some of the values of X will be 8,17,-1,-10 etc.
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