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Question

Miko has three pieces of string with lengths of 140 cm, 168 cm and 210 cm.

She wants to cut all three pieces of string into smaller pieces of equal length such that there is no leftover string.

(a) What is the greatest possible length of each of the smaller pieces of string?

(b) How many smaller pieces of string can she get altogether?



Answer 1

Hi Bennet,

Miko has three pieces of string with lengths of 140 cm, 168 cm and 210 cm.

She wants to cut all three pieces of string into smaller pieces of equal length such that there is no leftover string.

(a) What is the greatest possible length of each of the smaller pieces of string?

(b) How many smaller pieces of string can she get altogether?

Given:

1. 3 lengths of string 140cm 168cm 210cm 
2. Cut into equal length
3. no leftover string

Find:

1. Greatest length of string
2. Number of pieces of string

This problem is asking for a way to cut 3 different lengths of string into smaller pieces of the same length.

You could cut them all into 1 cm pieces and be done, but, they specifically ask for the largest possible length of a piece that would work. They are asking you to divide each string.

What you are looking for is the Greatest Common Factor of the 3 lengths of string. That way they would all but cut into the same length and have the greatest length possible.

GCF

Prime factorization of

140 = 2•2•5•7

168 = 2•2•2•3•7

210 = 2•3•5•7

The factors common to all 3 numbers are 2 and 7. The GCF would be 2•7=14

So the length of piece that would work would be 14 cm

The number of pieces

140 ÷ 14= 10

168 ÷ 14 = 12

210 ÷14 = 15

Total Number of Pieces: 10+12+15 = 37 Pieces

Hope this helps :)