# Proofs of rules of divisibility

• Jan 23rd 2010, 11:42 PM
Proofs of rules of divisibility
Hi! Can anybody pls prove the rules of divisibility for 4, 5,6,9, & 11 using modular arithmetic if possible.

I don't really get the proofs I searched from the net. Thanks! :D
• Jan 24th 2010, 06:59 AM
Dinkydoe
Quote:

Hi! Can anybody pls prove the rules of divisibility for 4, 5,6,9, & 11
Can you be more specific? . I'm not quite sure what you mean. Do you want to look at residu-classes modulo - these numbers?
• Jan 24th 2010, 10:47 AM
Moo
Proofs of divisibility, do you mean :

- 4 : last two digits form a number which is a multiple of 4
- 5 : ends by 0 or 5
- 6 : multiple by 2 & 3
- 9 : sum of digits makes a multiple of 9
- 11 : difference of alternate sums is a multiple of 11

?

If so, what specifically don't you understand ?
For 4, write the number as 100k+..
For 5, write the number as 10k+.
For 6, chinese remainder theorem
For 9, write the number as a linear combination of powers of 10, and while working modulo 9, it should be obvious
For 11, same thing as 9