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maths

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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?

  • maths - ,

    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.

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