Find the greatest possible length which can be used to measure exactly the length 7 m,

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.

Solution:

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:

$700=2 \times 2 \times 5 \times 5 \times 7=2^{2} \times 5^{2} \times 7$

$385=5 \times 7 \times 11$

$1295=5 \times 7 \times 37$

$\therefore \mathrm{HCF}=5 \times 7=35$

Hence, the greatest possible length is 35 cm.