OT: weird numbers

This works with the number 3 and the number 9.
Is 987659387043185671335 divisible by 9? Add up each digit: 9+8+7+6+5+9+3+8+7+0+4+3+1+8+5+6+7+1+3+3+5 = 108 Add up each digit of that: 1+0+8 = 9. 9 is divisible by 9, so so is 987659387043185671335.
If you can give me a reason why this works, you're cleverer than I am.
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On 03/27/2016 03:57 PM, Mr Macaw wrote:

Yes, here is the result
1.097399319×10²⁰
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If you do it my way you don't need a calculator.
-- "Okay, okay, I take it back! UnFuck you!"
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On 03/27/2016 04:16 PM, Mr Macaw wrote:

Sheesh...I worked with a guy who could probably not calculate anything more difficult than 2 x 2 = 4 unless he used a calculator
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Is that in merca?
-- 5 Brits were injured last year in accidents involving out of control Scalextric cars.
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On 03/27/2016 06:00 PM, Mr Macaw wrote:

Hugh betcha
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On Sunday, March 27, 2016 at 5:07:38 PM UTC-4, philo wrote:

I presume he really means evenly divisible.
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That's what divisible means.
-- Acupuncture is a jab well done.
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That's what divisible means.
-------------
no.
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Yes. If someone says "12 is divisible by 4", they mean "to produce a whole number". If someone said "13 is divisible by 4" they would be incorrect.
-- If you own a 3,000 machine gun and a 5,000 rocket launcher, but you can't afford shoes, you may be a Muslim.
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Yes. If someone says "12 is divisible by 4", they mean "to produce a whole number". If someone said "13 is divisible by 4" they would be incorrect.
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no.
https://en.wiktionary.org/wiki/evenly_divisible
http://www.mathwarehouse.com/dictionary/D-words/definition-of-divisible.php
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"You just reminded me why my pure maths course at uni made me wish I was in engineering class."
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Indeed. But engineering classes understood what is meant by "evenly divisible" too. It is a pretty basic concept. Like 3rd grade?
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On Sunday, March 27, 2016 at 8:34:40 PM UTC-4, taxed and spent wrote:

Your two references contradict each other. One says that just divisible means it has to be evenly divisible, ie with no remainder. That seems to be the correct definition, multiple source confirm it. So saying evenly divisible is not needed, it's already implied.
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Not required in more advanced engineering.
-- "Get as far away from the nuclear explosion as possible" - Rodney McKay, Stargate Atlantis.
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I'll illustrate the principle using a 3-digit number. Pick any three digits, and designate them as a, b, and c.
The sum of the digits is a + b + c; call this s. The value of the number is (100 * a) + (10 * b) + c; call this v.
The difference between the value of the number, and the sum of its digits, is v - s = (100a + 10b + c) - (a + b + c) = 99a - 9b = 9(11a - b)
Therefore, (v - s) must be a multiple of 9 (and hence of 3 also).
If s is a multiple of 3, and you add a multiple of 3 to it, the result must also be a multiple of 3, and likewise for multiples of 9.
Therefore if s is a multiple of 3 (or 9) then v = s + (v - s) is also a multiple of 3 (or 9).
For a four-digit number abcd, (v - s) = 999a + 99b + 9c = 9(111a + 11b + c) which is clearly a multiple of 9. And so on, for numbers having 5, 6, 7, etc. digits.
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