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remainder - shortcut method

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Director
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remainder - shortcut method [#permalink] New post 06 Mar 2006, 13:35
Hello,

if we want to get the remainder of a expression like:

(11*12*13*14)/5

is there a shortcut method?

thanks
Manager
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Re: remainder - shortcut method [#permalink] New post 06 Mar 2006, 17:21
allabout wrote:
Hello,

if we want to get the remainder of a expression like:

(11*12*13*14)/5

is there a shortcut method?

thanks


all I can think of is that a multiple of 5 must have a last digit that is 0 or 5
and its biggest possible mod is 4

if you take the last digits of 11*12*13*14

that would be 1*2*3*4 = 24
so the mod is 4

another example

like 11*12*13*18

1*2*3*8 = 48

mod is 3

I don't have a rigorous proof for this, but it works
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Re: remainder - shortcut method [#permalink] New post 06 Mar 2006, 20:11
conocieur wrote:
allabout wrote:
Hello,

if we want to get the remainder of a expression like:

(11*12*13*14)/5

is there a shortcut method?

thanks


all I can think of is that a multiple of 5 must have a last digit that is 0 or 5
and its biggest possible mod is 4

if you take the last digits of 11*12*13*14

that would be 1*2*3*4 = 24
so the mod is 4

another example

like 11*12*13*18

1*2*3*8 = 48

mod is 3

I don't have a rigorous proof for this, but it works


It's indeed a very good approach and i don't think there're still shorter ways :wink:
Director
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Joined: 17 Dec 2005
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 [#permalink] New post 07 Mar 2006, 00:49
conocieur

this approach works very well, thank you.
  [#permalink] 07 Mar 2006, 00:49
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remainder - shortcut method

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