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11 September, 20:50

Can you stop checking for factor pairs when you find a pair that repeats? Explain

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  1. 11 September, 22:35
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    Solution:

    Consider numbers which are Squares, cubes, fourths, fifths of some natural numbers.

    For example, Starting from squares of some natural number: 4,9,16,25,36,49,64 ...

    and their factors, which are 4 = 1 * 2*1*2

    9=1*3*1*3

    16=2*1*2*1*2*1*2*1

    25=1*5*1*5

    36=2*3*2*3

    64=2*4*2*4

    Now coming to cubic numbers

    8 = 1 * 2*1*2*1*2

    27 = 1*3*1*3*1*3

    3125 = 3 * 5*3*5*3*5

    So, the numbers whose factor pairs repeats are square, cubic, fourth, Fifth, Sixth and ... higher powers of natural Numbers.

    →→→So, we just need to check that whether those numbers whose factor pairs repeats are Squares, cubes or higher powers of natural numbers.
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