Posted by sunny on Friday, December 16, 2011 at 9:24am.
The first step is basically to factor 120175.
The obvious factor to do first is 5. this gives us 5 * 24035
Then factoring another 5 gives us 5 * 5 * 4807
Since 4807 obviously isn't divisible by 5 or 2, try 3.
So keep on trying the next biggest prime number (1,2,3,5,7,11,13,17...) turns out that 4807 is divisible by 11.
This gives us 5 * 5 * 11 * 437
Keep on going and you get
5 * 5 * 11 * 19 * 23
Just checking:
5 * 5 * 11 * 19 * 23 = 120175
Now converting these factors into letters.
You get the available letters EEKSW. this can be rearranged to be WEEKS.
However, remember that 5*5*11*19*23 can also be written as 25*11*19*23, since this also equals 120175.
This means the word could also have KSWY.
But you can't rearrange those letters to make a word.
So therefore the english word encoded as 120175 is WEEKS.
Basically, you factored the number, converted them into letters, and solved the anagram.