My Math Forum 3 digit numbers divisible by 7

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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 three-digit 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 $105+7(n-1)=994$ 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 3-digit 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 3-digit 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 $\frac{994\,-\,105}{7}\,+\,1\,=\,128$
 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 3-digit numbers, and every seventh number is divisible by 7. Hence the number of three-digit numbers divisible by 7 is $\lfloor \frac{900}{7} \rfloor= 128$, or $\lceil \frac{900}{7} \rceil= 129$. Since the first three-digit number divisible by 7 is 105, we add $105 + 7 \cdot 128= 1001$, which is not a three-digit number, so there are 128 three-digit numbers divisible by 7.
March 29th, 2012, 12:20 PM   #8
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Re:

Quote:
 Originally Posted by skipjack That could well be what was intended, but how would one know the number 994 without having already done a similar division by 7?
Using a calculator, divide 1000 by 7, subtract 142 and multiply the result by 7 to obtain 6. 1000 - 6 = 994.

 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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# how many three digit number are divisible by 7

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