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March 29th, 2012, 02:34 AM  #1 
Newbie Joined: Mar 2012 Posts: 9 Thanks: 0  3 digit numbers divisible by 7
Hi Friends How many threedigit numbers are divisible by 7? Can you tell me...please give me easier method than this http://www.youtube.com/watch?v=ZGYVFCivEcs 
March 29th, 2012, 04:44 AM  #2 
Senior Member Joined: May 2011 Posts: 501 Thanks: 6  Re: 3 digit numbers divisible by 7
I didn't look at the video, but I would use an arithmetic progression. The smallest three digit number that is divisible by 7 is 105 The largest is 994 So, using and solving for n will give the number of three digit numbers divisible by 7. 
March 29th, 2012, 06:59 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: 3 digit numbers divisible by 7
...or [(LAST  FIRST) / DIVISOR] + 1

March 29th, 2012, 07:07 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,927 Thanks: 2205 
After 98, every 7th natural number is divisible by 7. There are 900 3digit natural numbers, and 900 = 7 × 128 + 4. To avoid considering "+4", once can just start at 104 instead of 100. Since 100, 101, 102 and 103 are not multiples of 7, starting at 104 makes no difference to the final answer, which is therefore 128. For some strange reason, the video ignores the fact that 105 is a 3digit multiple of 7, and so (incorrectly) gives 127 as the answer. The formula given by Denis is unclear or does not have general validity. 
March 29th, 2012, 08:06 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: Denis' formula 
March 29th, 2012, 11:36 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,927 Thanks: 2205 
That could well be what was intended, but how would one know the number 994 without having already done a similar division by 7?

March 29th, 2012, 11:50 AM  #7 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: 3 digit numbers divisible by 7
Denis' formula is just what you get when you solve the equation given by Galactus for n. You have to find the numbers 105 and 994. Personally, this is what I would do: There are 900 3digit numbers, and every seventh number is divisible by 7. Hence the number of threedigit numbers divisible by 7 is , or . Since the first threedigit number divisible by 7 is 105, we add , which is not a threedigit number, so there are 128 threedigit numbers divisible by 7.

March 29th, 2012, 12:20 PM  #8  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: Quote:
 
March 29th, 2012, 12:50 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: 3 digit numbers divisible by 7
Mais oui: I was assuming low,high were givens...but if not, no problem(!): FLOOR[(999  100) / 7] = 128 
March 29th, 2012, 12:57 PM  #10 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: 3 digit numbers divisible by 7
7 × 150 = 1050, so it is not difficult to see that 7 × 142 = 994. (unless you are me! )


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