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 December 13th, 2011, 01:54 AM #1 Senior Member   Joined: Jul 2011 Posts: 402 Thanks: 16 no. of digit The no. which is of the form $34x5y,$ which is divisible by $36$ where $x,\;y$ are digits.
December 13th, 2011, 03:31 AM   #2
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Re: no. of digit

Quote:
 Originally Posted by panky The no. which is of the form $34x5y,$ which is divisible by $36$ where $x,\;y$ are digits.
x=4 and y=2, that is, 34452 or x=0 and y=6, that is, 34056

 December 13th, 2011, 09:39 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,799 Thanks: 970 Re: no. of digit Also x=9, y=6: 34956
 December 13th, 2011, 09:45 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs Re: no. of digit If a number is divisible by 36 then it is divisible by 4 and 9. To be divisible by 4, then the number formed by the two rightmost digits will be divisible by 4. 52 and 56 are divisible by 4, so y may be either 2 or 6. If a number is divisible by 9, then the sum of its digits is divisible by 9. 3 + 4 + 5 = 12, so x + y = 6 or x + y = 15. So we have 3 possibilities: (x,y) = (0,6), (4,2), (9,6) 34056 34452 34956

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