maths
posted by sunny .
in a common coding method each of the letters of the alphabet is replace by the number denoting its usual place in alphabetical order, a bird is then encoded by multiplying the number representing the letter of the word. find an english word that is encoded as 120175?

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.