Question

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

Answer 1

The three given lengths are 7m (700cm), 3m 85cm (385cm) and 12m 95m (1295cm). (∵1m = 100cm).
∴ Required length = HCF (700, 385, 1295)
Prime factorization:
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 35cm.