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?

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