Find the greatest possible length which can be used to measure exactly the…

To find the greatest possible length that can measure given lengths exactly, you need to find the Highest Common Factor (H.C.F.) of the measurements.

Step-by-Step Calculation
1. Convert all measurements to the same unit (centimeters):

4 m 95 cm = 400 cm + 95 cm = 495 cm

9 m = 900 cm

16 m 65 cm = 1600 cm + 65 cm = 1665 cm

2. Find the H.C.F. of 495, 900, and 1665:

Prime factorization:

495 = 5 * 9 * 11 = 3^2 * 5 * 11

900 = 9 * 100 = 3^2 * 2^2 * 5^2

1665 = 5 * 333 = 5 * 9 * 37 = 3^2 * 5 * 37

The H.C.F. is determined by the lowest power of common prime factors:

Common factors: 3^2 and 5^1

H.C.F. = 9 * 5 = 45 cm.