Of Course, But Maybe?

Number Theory Level 1

$\large 123456789$

The number above is divisible by 9.
If I rearrange the positions of these digits to form a different number,
would it still be divisible by 9?

Yes, always No, never Sometimes, but not always

2 solutions

Ryan Shi
Sep 6, 2016

Divisibility rule of 9: The sum of all the digits in any number MUST be a multiple of 9. By rearranging the digits the sum is still the same, hence the number is still divisible by 9.

So trippy. I don't understand the theorem but it definitely works...

Tony B - 4 years, 9 months ago

Prokash Shakkhar
Dec 17, 2016

We can use the divisibility rule of $9$ .. An integer $abcd$ will be divisible by $9$ if and only if $a+b+c+d$ is divisible by $9$ .. Sum of the digits doesn't vary due to the rearrangement of the digits.. So, $123456789$ is divisible by $9$ in its every rearrangement.. That is $9|(123456789)$

Of Course, But Maybe?

2 solutions

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