Question

Find the length of the longest rope that can be used to measure exactly the ropes of length 1 m 20 cm, 3 m 60 cm and 4 m

Answer 1

1 m 20 cm = 120 cm

3 m 60 cm = 360 cm

4 m = 400 cm

This is a HCF related problem.

So, we need to find the HCF of 120, 360 and 400

2	120
2	60
2	30
3	15
	5

2	360
2	180
2	90
3	45
3	15
	5

2	400
2	200
2	100
2	50
5	25
	5

120 = 2 × 2 × 2 × 3 × 5

360 = 2 × 2 × 2 × 3 × 3 × 5

400 = 2 × 2 × 2 × 2 × 5 × 5

HCF = 2 × 2 × 2 × 5 = 40

The length of the longest rope = 40 cm