Question

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

Answer 1

The three given lengths are $7$ m $=700$ cm
$3$ m $85$ cm $=385$ cm and
$12$ m $95$ m$=1295$ cm
now the required length is HCF of $700,385$ and $1295.$
$700=2^2\times 5^2\times 7$
$385=5\times 7\times 11$
$1295=5\times 7\times 37$
HCF $(700,385$ and $1295)=5\times 7=35$
The greatest possible length is 35 cm