Q. 174.9( 22 Votes )

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 :

We know 1m = 100cm.


So,


7m = 700cm,


3m 85cm = 300 + 85 = 385cm,


and 12m 95cm = 1200 + 95 = 1295cm.


The greatest possible length that can measure all the three given lengths will be HCF of the lengths -


So HCF of 700, 385 and 1295 -


Prime factors of numbers are -


700 = 2 × 2 × 5 × 5 × 7


385 = 5 × 7 × 11


1295 = 5 × 7 × 37


HCF = 5 × 7 = 35.


So the greatest possible length that can be used = 35cm.


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