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 Goodies on facebook

Math Goodies Blog
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 0.04 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2015 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 25 Jan 2015