Question

I think it is cute.
If a number has a even amount of digits and given a certain type of symmetry, the number can be factored like this for example:
\[mnmnmn=n+m10+n10^2+m10^3+n10^4+m10^5 \\ =n(1+10^2+10^4)+m(10+10^3+10^5) \\ =n(1+10^2+10^4)+10m(1+10^2+10^4) \\ =(1+10^2+10^4)(10m+n)\]
Do you know of any other cute similar ways to factor numbers?

Answer 1

:O yeah its amazing ! how did u get it ?

Answer 2

do u have something similar to odd numbers of digits ?

Answer 3

i wished

Answer 4

me too :(

Answer 5

mnmnmnmn... = mn(101010101...)
mnomnomnomno... = mno(1001001001001...)

this is really a cute trick xD

Answer 6

I kinda closed this like 6 days right after opening it thinking it was not that cool :p

Answer 7

\(\)

Answer 8

but i would really like to find a factorization for odd digit numbers with the that symmetry

Answer 9

don't think it is possible though to factored like that though

Answer 10

and yeah @ganeshie8 that is a cool trick too

Answer 11

\[nmn=n 10^2+m10+n\]
if there were two factors of n^2 that had product n^2 and sum m we could do that whole factor by grouping thing

Answer 12

343 is also factorable and can't be factored like that though

Answer 13

3103 can be factored like that though

\[3103=3 +10 \cdot 10+3 \cdot 10^2 \\ 3+9 \cdot 10 +1 \cdot 10+3 \cdot 10^2 \\ 3(1+3 \cdot 10)+10(1+3 \cdot 10) \\ (3+10)(1+3 \cdot 10)\]

Answer 14

\[363=3+6 \cdot 10+3 \cdot 10^2 \\ 3+3 \cdot 10+3 \cdot 10+3 \cdot 10^2 \\ 3(1+10)+3 \cdot 10(1+10) \\ (1+10)(3+3 \cdot 10) \\ 3(1+10)^2 \]

Answer 15

yes by this now i wont even think of any even digits symmetry ;) as prime thanks allot

Answer 16

made my day actually :3

Answer 17

it made my a week ago day when i saw this method for the first time in a @myininaya 's question ;)

Answer 18

oh

Answer 19

now i lost my day lol

Answer 20

it was about factoring some big number though.. i dont seem to remember the exact number. .

Answer 21

lol

Answer 22

ok

Answer 23

i think you confused two people

Answer 24

http://openstudy.com/users/freckles#/updates/54ab17aae4b0b83d9dca4479

Answer 25

it was @freckles

Answer 26

Ahh it was you, i was searching in myininaya's Qs and for some weird reason i thought she has deleted that question lol

Answer 27

Some people tell me I look like myininaya all the time. I think it is weird.

Answer 28

ppl tell me i look like some Angelina i dont find it weird at all :P
(jk)

Answer 29

angelina jolie?

Answer 30

i used to think she was hot

Answer 31

she is smart

Answer 32

i don't know anything about her brain

Answer 33

but she looks smart

Answer 34

actually she is smart , idk she has something

Answer 35

but i was jk before lol

Answer 36

tbh i thought ur a girl @freckles

Answer 37

i could be

Answer 38

:P what ever

Answer 39

i will go either way
it just depends which one is more beneficial at the time
or the one I think is more humorous at the time

Answer 40

\(\pi\)

Answer 41

interesting ....

Answer 42

i should specialize in human study rather than math xd

Answer 43

I want to factor 343
like maybe there is a base that we can convert it to such that it is factorable in that base

Answer 44

i mean i know 343 is factorable
i just want to find a similar way to the way i have been factoring

Answer 45

hmm 343 been solved try

34343

Answer 46

for example:

\[10 \text{ can't be factored the way I mentioned unless I write } 10 \text{ as } 1010_2 \\ 1010_2=0 \cdot 2^0+1 \cdot 2^1 +0 \cdot 2^2 +1 \cdot 2^3 \\ =1(2 \cdot 1+2^3)+0(2^0+2^2) \\ =1 \cdot 2(1+2^2)+0(1+2^2) \\ =(1+2^2)(1 \cdot 2+0) \\ = (1+4)(2+0) \\ =(5)(2) \\\]

Answer 47

hmmm I wonder if we could have done the same thing in base 5

Answer 48

got what ur saying