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July 8th, 2017, 11:03 PM   #1
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Question Complete divisor of a number

Hi all,
I am having such a naïve problem, yet unable to comprehend it now:

$\displaystyle 21904/2 $ should come out to be $\displaystyle 1952 $ plainly, but calculator suggests it to be $\displaystyle 10952 $.

What's the rule here?

Last edited by skipjack; July 9th, 2017 at 12:07 AM.
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July 8th, 2017, 11:25 PM   #2
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If 21904/2 = 1952, then 1952(2) = 21904, but that isn't true.

21904 / 2 = 10952 is true though because 21904 = 10952(2).

I think you may have forgot a 0 somewhere in your solution, because 1952 and 10952 are similar-looking.

Last edited by skipjack; July 9th, 2017 at 12:07 AM.
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July 9th, 2017, 04:42 AM   #3
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Quote:
Originally Posted by Choboy11 View Post
If 21904/2 = 1952, then 1952(2) = 21904, but that isn't true.

21904 / 2 = 10952 is true though because 21904 = 10952(2).

I think you may have forgot a 0 somewhere in your solution, because 1952 and 10952 are similar-looking.
Sorry, what I am asking is the reason for "ZERO" in quotient in below image at link provided.
What's the rule for it?
Why "Zero" comes in quotient while there isn't a need? - Album on Imgur

Last edited by skipjack; July 9th, 2017 at 05:04 AM.
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July 9th, 2017, 05:11 AM   #4
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There is a need. When 1 and 9 are brought down, the 0 is because the 1 isn't large enough to have a non-zero multiple of 2 subtracted from it. Subtracting a zero multiple of 2 is omitted (as subtracting zero has no effect), but 0 has to be entered in the quotient.
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July 9th, 2017, 05:17 AM   #5
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Quote:
Originally Posted by skipjack View Post
Subtracting a zero multiple of 2 is omitted (as subtracting zero has no effect), but 0 has to be entered in the quotient.
So,what you mean is : It's true for all such cases where zero multiple of a'n' is omitted e.g. for 3,4,5 etc?
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July 9th, 2017, 09:48 AM   #6
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4 divided by 7 = 0 remainder 4

May I ask: are you serious?
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July 29th, 2017, 04:04 AM   #7
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Long division is typically taught in fourth or fifth grade, to 9 or 10 year olds. Of course, we have no way of knowing how old you are.
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July 29th, 2017, 12:42 PM   #8
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Quote:
Originally Posted by Jeddi View Post
Sorry, what I am asking is the reason for "ZERO" in quotient in below image at link provided.
What's the rule for it?
Why "Zero" comes in quotient while there isn't a need? - Album on Imgur
The zero comes in because

$20000 < 21904 < 22000 \implies$

$\dfrac{20000}{2} < \dfrac{21904}{2} < \dfrac{22000}{2} \implies$

$10000 < \dfrac{21904}{2} < 11000.$
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