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 :)

4 L A T E S T R E P L I E S (Newest First)

Ultraglide

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

Subhotosh Khan

Posted - 09/28/2009 : 10:07:13

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

Katy

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

Mrspi

Posted - 09/25/2009 : 21:42:08

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

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.

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.