When a natural number ‘a’ is divided by another natural number ‘b’, if the quotient is ‘t’ and remainder is ‘r’ then ‘a’ can be uniquely expressed as a = tb + r where 0 LaTeX: \le≤r LaTeX: <<b , a > b. Let a = 666………6 consisting of 666 sixes. Then......
For b = 11, the value of r is_____
Answers
Given : a = tb + r a = 666………6 consisting of 666 sixes. b =50
To find : Value of r
Solution:
a = tb + r
a = 666,..............6 Consisting of 666 times 6
b = 11
Divisibility rule of 11
The Divisibility Rule of Eleven is that you must subtract and then add the digits in an alternating pattern from left to right
and resultant should be divisible by 11
6 - 6 + 6 - 6 + 6 - 6 + ..................................................+ 6 - 6 ( as there are 666 times 6 hence even time
(6 - 6) + (6 - 6) + (6 - 6) +...........................................+ (6 - 6) 333 times
0 + 0 + 0 +...........................+ 0 333 times
= 0
Hence 666………6 consisting of 666 sixes is divisble by 11
Hence value of r = 0
666………6 consisting of 666 sixes. = 11 ( 606060...............606) + 0
60 is repeated 332 times
Value of r = 0
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