Question

Find the greatest possible length which can be used to measure exactly the length 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 cm (1295 cm). (∵ 1 m = 100 cm)
∴ Required length = HCF (700, 385, 1295)
Prime factorisation:
700 = $2\times 2\times 5\times 5\times 7=2^2\times 5^2\times 7$
385 = $5\times 7\times 11$
1295 = $5\times 7\times 37$
∴ HCF = $5\times 7$ = 35
Hence, the greatest possible length is 35 cm.