Question

Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm. 

(1) 45 

(2) 35 

(3) 25 

(4) 15

Answer 1

Correct option is (1) 45

Convert all measurements to Centimeters.

4 m 95 cm = 495 cm

9 m = 900 cm

16 m 65 cm = 1665 cm

Prime factorization of each length.

495 = 3² x 5 x 11

900 = 2² x 3² x 5²

1665 = 3² x 5 x 37

HCF = 3² x 5

= 9 x 5

= 45

Hence, required length = 45 cm.