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Show that any number of the form ABCABC (e.g. 356356) is divisible by 13.

Show that any number of the form ABCABC (e.g. 356356) is divisible by 13.
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Show that any number of the form ABCABC (e.g. 356356) is divisible by 13.

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User David Carlson
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1 Answer

2 votes

We could write such a number as


10^5a+10^4b+10^3c+10^2a+10b+c


=10^2(10^3+1)a+10(10^3+1)b+(10^3+1)c


=(10^3+1)(100a+10b+c)


10^3+1=1001=13\cdot77 so we're done.

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User Tshalif
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