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Katy
Junior Member

6 Posts

 Posted - 09/25/2009 :  20:07:24 Find the smallest positive integer that gives a remainder of 2 when divided by either 3 or 7, and gives a remainder of 3 when divided by 5.any help is greatly appreciated thanks :)

Mrspi

USA
998 Posts

 Posted - 09/25/2009 :  21:42:08 quote:Originally posted by KatyFind the smallest positive integer that gives a remainder of 2 when divided by either 3 or 7, and gives a remainder of 3 when divided by 5.any help is greatly appreciated thanks :)If the integer you're looking for gives a remainder of 2 when it is divided by 3, then it must be 2 MORE than a multiple of 3...I'll make a multiplication table for the 3's, and add two to each product3*1 = 3 + 2 = 53*2 = 6 + 2 = 83*3 = 9 + 2 = 113*4 = 12 + 2 = 143*5 = 15 + 2 = 173*6 = 18 + 2 = 203*7 = 21 + 2 = 233*8 = 24 + 2 = 26Ok, if we need to go farther than that, we can do it later.the integer you're looking for gives a remainder of 2 when it is divided by 7, also. So, I'll make a multiplication table for 7, and add 2 to each product.7*1 = 7 + 2 = 97*2 = 14 + 2 = 167*3 = 21 + 2 = 237*4 = 28 + 2 = 307*5 = 35 + 2 = 37HMMMMMM...I see a possible candidate!! 23 is in BOTH of those tables!!Could 23 be the number we're looking for? Let's check the last part, which says that "our number" has a remainder of 3 when divided by 5.We're looking at 23...23 divided by 5 is 4 remainder 3Looking good!! And since there are NO smaller positive integers in the tables for 3 and 7, 23 must be the smallest positive integer which has a remainder of 2 when divided by 3 or 7, and a remainder of 3 when divided by 5.

Katy
Junior Member

6 Posts

 Posted - 09/26/2009 :  16:20:33 Thank you soooo much!!!

Subhotosh Khan

USA
9114 Posts

 Posted - 09/28/2009 :  10:07:13 quote:Originally posted by KatyFind the smallest positive integer that gives a remainder of 2 when divided by either 3 or 7, and gives a remainder of 3 when divided by 5.any help is greatly appreciated thanks :)the number X = 3m + 2 and X = 7n + 2then3m + 2 = 7n + 23m = 7mm = 7 and n = 3 are the smallest solution for the equation above (since 3 and 7 are relatively prime)then X = 3*7 + 2 = 23

Ultraglide

278 Posts

 Posted - 01/13/2010 :  17:00:10 Just a note to Mrspi, you used bad form when writing3*1=3+2=5etc.
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