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

Answer:

Given lengths are 7m (700cm), 3m 85cm (385cm) and 12m 95m (1295cm).

The required length = HCF (700, 385, 1295)

Using prime factorization,

700 = 2 × 2 × 5 × 5 × 7 = 2² × 5² × 7

385 = 5 × 7 × 11

1295 = 5 × 7 × 37

∴ HCF = 5 × 7 = 35

The greatest possible length = 35cm.