testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
Username:
Password:
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Basic Math and Pre-Algebra
 integers
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

Katy
Junior Member

Canada
6 Posts

Posted - 09/25/2009 :  20:07:24  Show Profile  Reply with Quote
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 :)
Go to Top of Page

Mrspi
Advanced Member

USA
998 Posts

Posted - 09/25/2009 :  21:42:08  Show Profile  Reply with Quote
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.
Go to Top of Page

Katy
Junior Member

Canada
6 Posts

Posted - 09/26/2009 :  16:20:33  Show Profile  Reply with Quote
Thank you soooo much!!!
Go to Top of Page

Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 09/28/2009 :  10:07:13  Show Profile  Reply with Quote
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
Go to Top of Page

Ultraglide
Advanced Member

Canada
299 Posts

Posted - 01/13/2010 :  17:00:10  Show Profile  Reply with Quote
Just a note to Mrspi, you used bad form when writing
3*1=3+2=5
etc.
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.06 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 21 May 2014