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Katy
Junior Member
Canada
6 Posts |
 Posted - 09/25/2009 : 20:07:24
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| 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 :) |
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Mrspi
Advanced Member
USA
998 Posts |
Posted - 09/25/2009 : 21:42:08
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quote:
Originally posted by Katy
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 :)
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 product
3*1 = 3 + 2 = 5
3*2 = 6 + 2 = 8
3*3 = 9 + 2 = 11
3*4 = 12 + 2 = 14
3*5 = 15 + 2 = 17
3*6 = 18 + 2 = 20
3*7 = 21 + 2 = 23
3*8 = 24 + 2 = 26
Ok, 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 = 9
7*2 = 14 + 2 = 16
7*3 = 21 + 2 = 23
7*4 = 28 + 2 = 30
7*5 = 35 + 2 = 37
HMMMMMM...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 3
Looking 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. |
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Katy
Junior Member
Canada
6 Posts |
Posted - 09/26/2009 : 16:20:33
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| Thank you soooo much!!! |
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Subhotosh Khan
Advanced Member
USA
9114 Posts |
Posted - 09/28/2009 : 10:07:13
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quote:
Originally posted by Katy
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 :)
the number X = 3m + 2 and X = 7n + 2
then
3m + 2 = 7n + 2
3m = 7m
m = 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 |
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Ultraglide
Advanced Member
Canada
276 Posts |
Posted - 01/13/2010 : 17:00:10
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Just a note to Mrspi, you used bad form when writing
3*1=3+2=5
etc. |
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Interactive Math Goodies Software
integers
