Question

What are the factors of 45855?

Answer 1

first try dividing by 3 because this is an odd number

Answer 2

or maybe try dividing by 5 because the last digit is 5

Answer 3

yes that makes sence
I suggested 3 because the digits add up to 27

Answer 4

Ahh i see.. then it is also divisible by 9

Answer 5

I remembered this rule from way back
- if you keep adding the digits until only one remains and its 3,6 or 9 then the number is divisible by 3
2 + 7 = 9 of course

Answer 6

I've forgotten the proof though!

Answer 7

than u can divide by 15

Answer 8

yes

Answer 9

thats very interesting
so you're adding digits in 27 again...
and keep repeating this until u get a single digit nice

Answer 10

yes

Answer 11

by 15 and than by 3 or 45 from the beginning

Answer 12

that works because \(10\equiv 1 \pmod{3}\)

\[\begin{align}45855 &= 4*10^{4} + 5*10^3 + 8*10^2+5*10^1 + 5\\ &\equiv 4*1^{4} + 5*1^3 + 8*1^2+5*1^1 + 5\pmod{3}\\&\equiv 4+5+8+5+5\pmod{3} \end{align}\]

Answer 13

±1, ±3, ±5, ±9, ±15, ±45, ±1019, ±3057, ±5095, ±9171, ±15285, ±45855

Answer 14

that's a clever proof ' I'll have to learn more about modular arithmetic. Is there a good website teaching it?

Answer 15

1019 is prime

Answer 16

@rational do you know a good source on modular arithmetic?

Answer 17

http://www.math.kent.edu/~soprunova/34001s11/notes_week11.pdf

it has a short tutorial talking about pure congruences w/o any other distractions @welshfella

Answer 18

ok thanks very much