Given: The length, breadth and height of a room are 8 m and 25 cm, 6 m 75 cm and 4 m 50 cm.

To find: the longest rod which can measure the three dimensions of the room exactly.

Solution:

To find the length of largest rod, we should find HCF of 8m and 25 cm, 6 m 75 cm and 4 m 50 cm

As 1 m = 100 cm

⇒ 8m and 25 cm = 8 × 100 cm + 25 cm
= 800 cm + 25 cm
= 825 cm

⇒ 6 m and 75 cm = 6 × 100 cm + 75 cm
= 600 cm + 75 cm
= 675 cm

⇒ 4 m and 50 cm = 4 × 100 cm + 50 cm
= 400 cm + 50 cm
= 450 cm

Length = 825 cm; Breadth = 675 cm; Height = 450 cm

Prime factors of 825 = 3 × 5 × 5 × 11

Prime factors of 675 = 3 × 3 × 3 × 5 × 5

Prime factors of 450 = 2 × 3 × 3 × 5 × 5

Therefore HCF of 825, 675 and 450 is: 3 × 5 × 5 = 75

Hence, the length of rod is: 75 cm

NOTE: Always find the HCF of the given values to find their maximum.

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