What is the greatest length that can measure the lengths 7 m, 3.85 m and 12.95 m exactly?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 35 cm
A length measures another exactly when it divides it with nothing left over, so the greatest length that measures all three is their HCF. The lengths are first written in the same unit, centimetres.
7 m \(=700\) cm, 3.85 m \(=385\) cm, 12.95 m \(=1295\) cm
\(700=2^{2}\times5^{2}\times7\)
\(385=5\times7\times11\)
\(1295=5\times7\times37\)
Common factors: 5 and 7, so HCF \(=5\times7=35\)
The greatest measuring length is 35 cm.