remainder of X
Calculus
Level
2
- There is a number X:
- X=1234...201620172018
- (123456 to 2018)
- Now, what is the remainder of X if X is divided by 9?
The answer is 3.
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1 solution
- As the special formula of multiple of 9 are
- 9x1 = 9,9 = 9
- 9x2 = 18,1+8 =9
- 9x3 = 27,2+7 =9
- 9x4 = 36,3+6 = 9
- ...
- s e p a r a t i o n l i n e
- We only need to add all numbers in X (1,2,3,4,...,2016,2017,2018) to find the number to be divided by 9
- 2 ( F i r s t N u m b e r + L a s t N u m b e r ) ∗ L a s t N u m b e r
- = 2 ( 1 + 2 0 1 8 ) ∗ 2 0 1 8
- =2037171
- s e p a r a r t i o n l i n e
- Then, we divide it by 9:
- 2037171/9
- =226352 1 0 3
- s e p a r a t i o n l i n e
- Since we are looking for the remainder of X,
- we do not care about the actual value,
- and we only care about the fraction formed.
- Therefore, the remainder is 3 .
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