## divide it

For students of class 11-12 (age 16+)
Rafe
Posts: 22
Joined: Wed Oct 24, 2012 11:25 am

### divide it

show that the number abbcca is divided by 11 for any value of a,b,c within 1-9
Last edited by Rafe on Sat Dec 29, 2012 11:30 am, edited 1 time in total.

SANZEED
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm

### Re: divide it

Rafe wrote:show that the number abbcca is divided by 7 for any value of a,b,c within 1-9
I think this statement is incorrect. For a counter example is $211332$ where $a=2,b=1,c=3$.
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Fahim Shahriar
Posts: 138
Joined: Sun Dec 18, 2011 12:53 pm

### Re: divide it

The statement is not true at all. If you said $abcabc$, then it would be divisible by $7$.
Name: Fahim Shahriar Shakkhor
Notre Dame College

SANZEED
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm

### Re: divide it

Fahim Shahriar wrote:The statement is not true at all. If you said $abcabc$, then it would be divisible by $7$.
Again,with the criteria of divisibility by $7$, we can also show that the first number $abbcca$ is dividible by $7$, if the number $3c-2a-b$ is divisible by $7$. That's how I find examples like $7|211442$ and counter-example $211332$.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

Rafe
Posts: 22
Joined: Wed Oct 24, 2012 11:25 am

### Re: divide it

sorry friends.i have corrected that

$a-b+b-c+c-a=0\equiv 0(\bmod \; 11)$ so by the divisibility rule of $11$ we can conclude that $(abbcca)_{10}\equiv 0(\bmod \; 11)$