## hba Group Title When n is divided by 12,the remainder is 6.What is the remainder when n is divided by 6 ? one year ago one year ago

1. waterineyes Group Title

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

2. hba Group Title

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

3. waterineyes Group Title

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

4. waterineyes Group Title

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 Group Title

and *remainder as 0..

6. hba Group Title

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

7. waterineyes Group Title

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

8. Rosh007 Group Title

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

9. waterineyes Group Title

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 Group Title

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 Group Title

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

12. jobs Group Title

tamtoan got the correct way..

13. hba Group Title

i have options so we can put them and check ?

14. waterineyes Group Title

Sure..

15. jobs Group Title

yep....

16. waterineyes Group Title

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 Group Title

*leave

18. Rosh007 Group Title

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 Group Title

0,1,2,3

20. hba Group Title

^ options ?

21. hba Group Title

Now you guys have pretty confused me lol

22. hba Group Title

@waterineyes Now tell me the math behind this :(

23. Rosh007 Group Title

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

24. waterineyes Group Title

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

25. Rosh007 Group Title

followed by tamtoan's first response

26. hba Group Title

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

27. waterineyes Group Title

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

28. hba Group Title

yes

29. waterineyes Group Title

Now can you factor out 6 from that ??

30. hba Group Title

no.

31. hba Group Title

how to do that ?

32. waterineyes Group Title

By using distributive property??

33. waterineyes Group Title

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

34. hba Group Title

n=6(2q+1)

35. waterineyes Group Title

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 Group Title

ok

37. hba Group Title

so here the factors are 6 and 2q+1

38. waterineyes Group Title

Good going..

39. waterineyes Group Title

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 Group Title

more..

41. waterineyes Group Title

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 Group Title

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

43. waterineyes Group Title

More ??

44. waterineyes Group Title

Still not getting tell me @hba

45. hba Group Title

gotcha:D

46. hba Group Title

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

47. hba Group Title

what next ?

48. waterineyes Group Title

You have to find remainder no??

49. waterineyes Group Title

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

50. waterineyes Group Title

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

51. waterineyes Group Title

Net got crushed??

52. hba Group Title

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

53. waterineyes Group Title

Yes it is...