## hba 3 years ago When n is divided by 12,the remainder is 6.What is the remainder when n is divided by 6 ?

1. waterineyes

According to first statement : n = 12q + 6 According to second statement: n = 6p + r We are to find r..

2. hba

I am not very sure on how you generated the statements ?Please explain.

3. waterineyes

See, there is formula : $Dividend = Divisor \times Quotient + Remainder$

4. waterineyes

If I say 4 divides 12 leaving quotient as 3 and 0 : Then we can represent it as : $12 = 4 \times 3 + 0$

5. waterineyes

and *remainder as 0..

6. hba

Ok then how is the Q(x) p and q

7. waterineyes

I have assumed them as p and q in that two cases because we don't know them..

8. Rosh007

@waterineyes what you given is true but there is two eqns and 3 unknowns... am I wrong?

9. waterineyes

Yes we have 3 unknowns and this time I am remembering @mukushla because he is expert in finding 3 unknowns out of 1 equation given only.. Ha ha ha ha...

10. tamtoan

n = 12q + 6 = 6(2q +1) so n is a multiple of 6 ...:) when you that a multiple of 6 divide 6...is there a remainder ? :)

11. jobs

when 6,,,...remainder should be 0 !!!!!

12. jobs

tamtoan got the correct way..

13. hba

i have options so we can put them and check ?

14. waterineyes

Sure..

15. jobs

yep....

16. waterineyes

18, 30, 42, 54 all leaves remainder as 6 when divided by 12.. So, you can easily see that they all are fully divided by 6, leaving remainder as 0..

17. waterineyes

*leave

18. Rosh007

Thanks to all........ I never think of bunchy equations but only facts... My bad.... i thought how it is possibl to solve it... my bad,... but thanks I got it

19. hba

0,1,2,3

20. hba

^ options ?

21. hba

Now you guys have pretty confused me lol

22. hba

@waterineyes Now tell me the math behind this :(

23. Rosh007

I think @hba will be able to comprehend Ida behind it when you again check the first response of waterineyes

24. waterineyes

Are you still not able to find the correct choice??

25. Rosh007

followed by tamtoan's first response

26. hba

Well the answer is 0 but i could not understand the math behind it :(

27. waterineyes

Till here you got : $n = 12q + 6$

28. hba

yes

29. waterineyes

Now can you factor out 6 from that ??

30. hba

no.

31. hba

how to do that ?

32. waterineyes

By using distributive property??

33. waterineyes

$ab + ac = a(b+c)$

34. hba

n=6(2q+1)

35. waterineyes

Yep. Now if I say that $$n = 3\times 4$$ then it means that 3 and 4 are the factors of n.. Okay??

36. hba

ok

37. hba

so here the factors are 6 and 2q+1

38. waterineyes

Good going..

39. waterineyes

And you must remember that factors divide the number fully leaving NO REMAINDER BEHIND.. If $$n = 3 \times 4$$ then 3 and 4 both will divide n fully leaving remainder as 0.. Getting or more explanation you want??

40. hba

more..

41. waterineyes

See, here $$3 \times 4 = 12$$ So here n = 12.. Now divide 12 by 3 first : Quotient - 4 Remainder - 0 Now divide 12 by 4: Quotient - 3 Remainder - 0 What did you get as remainder??

42. waterineyes

It means that factors of any number will divide it fully leaving No Remainder.. It is obvious hba..

43. waterineyes

More ??

44. waterineyes

Still not getting tell me @hba

45. hba

gotcha:D

46. hba

So, 6/n=0 and 6/2q+1 = 0

47. hba

what next ?

48. waterineyes

You have to find remainder no??

49. waterineyes

That you have found I think... Why do you want to go next in this??

50. waterineyes

Sorry, remainder of n/6 will be 0.. And not 6/n..

51. waterineyes

Net got crushed??

52. hba

Sorry some issue with my internet connection,So the answer is 0 @waterineyes

53. waterineyes

Yes it is...

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