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20 December, 01:29

You have two pieces of string. One is 8 cm long. The other is 20 centimeters long. You want to cut each piece if string into smaller pieces of equal length. Each length is to be a whole number of centimeters. List all the possible length of the shorter pieces. What is the greatest common length from these two lists?

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  1. 20 December, 01:33
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    ah, basically what length can you divide each string to get a certain length

    factor each

    8=2*2*2

    therefor:

    8=1*8=2*4=4*2=8*1

    so you can have 1 length of string 8cm long

    2 lengths of string 4cm long

    4 lengths of string 2cm long

    8 lengths of string 1cm long

    20cm string

    factor

    20=1*2*2*5

    so 20=1*20=2*10=4*5=5*4=10*2=20*1

    you can have 1 string 20cm long

    2 strings 10cm long

    4 strings 5cm long

    5 strings 4cm long

    10 strings 2cm long

    20 strings 1cm long

    we need greatest common length

    in 8cm stirng, we have 1,2,4,8

    in 20cm string, we have 1,2,4,5,10,20

    greatest common length is 4

    answer is 4cm

    alternately, you could have done this:

    8=2*2*2

    20=2*2*5

    common grooup is 2*2=4 so 4 is answer
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