Question

Determine the longest tape which can be used to measure exactly the lengths 7 m, 3 m 85 cm, and 12 m 95 cm.

Answer 1

The given lengths are:

7 meters = 7 × 100 cm = 700 cm

3 meters 85 cm = (3 × 100 + 85) cm = 385 cm

12 meters 95 cm = (12 × 100 + 95) cm = 1295 cm

The length of the required longest tape = H.C.F. of 700 cm, 385 cm, and 1295 cm.

We have,

2	700
2	350
5	175
5	35
7	7
	1

5	385
7	77
11	11
	1

5	1295
7	259
37	37
	1

So, 700 = 2 × 2 × 5 × 5 × 7 = 2² × 5² × 7

385 = 5 × 7 × 11

1295 = 5 × 7 × 37

∴ H.C.F. of 700, 385 and 1295 = 5 × 7 = 35

∴ The required length of the longest tape is 35 cm.