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March 29th, 2012, 02:34 AM   #1
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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
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March 29th, 2012, 04:44 AM   #2
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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.
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March 29th, 2012, 06:59 AM   #3
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Re: 3 digit numbers divisible by 7

...or [(LAST - FIRST) / DIVISOR] + 1
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March 29th, 2012, 07:07 AM   #4
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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.
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March 29th, 2012, 08:06 AM   #5
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Re: Denis' formula

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March 29th, 2012, 11:36 AM   #6
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That could well be what was intended, but how would one know the number 994 without having already done a similar division by 7?
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March 29th, 2012, 11:50 AM   #7
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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 , or . Since the first three-digit number divisible by 7 is 105, we add , which is not a three-digit number, so there are 128 three-digit numbers divisible by 7.
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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.
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March 29th, 2012, 12:50 PM   #9
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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
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March 29th, 2012, 12:57 PM   #10
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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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