The greatest length of the scale that can measure exactly 20 cm, 90 cm, 1 m 25 cm and 1 m 30 cm length is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 cm
A scale that measures each length a whole number of times must divide every length without a remainder, so the greatest such scale is the HCF of the lengths, all in the same unit.
Lengths in cm: 20, 90, 125, 130
\(20=2^{2}\times5\), \(90=2\times3^{2}\times5\), \(125=5^{3}\), \(130=2\times5\times13\)
The only factor common to all four is 5, so HCF \(=5\) cm