Question

Find the greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm and 12 m 95 cm.

Answer 1

The three given lengths are 7 m (700 cm), 3 m 85 cm (385 cm) and 12 m 95 m (1295 cm). (∵ 1 m = 100 cm).

∴ Required length = HCF (700, 385, 1295)

Prime factorisation:

700 = 2 × 2 × 5 × 5 × 7 = 2² × 5² × 7

385 = 5 × 7 × 11

1295 = 5 × 7 × 37

∴ HCF = 5 × 7 = 35

Hence, the greatest possible length is 35 cm.