The length, breadth and height of a room are 1050 cm, 750 cm and 425 cm respectively. Find the length of the longest tape which can measure the three dimensions of the room exactly

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Solution

1050 = 1 × 2 × 3 × 5 × 5 × 7 = 2¹ × 3¹× 5² × 7¹
750 = 1 × 2 × 3 × 5 × 5 × 5 = 2¹ × 3¹× 5³
425 = 1 × 5 × 5 × 17 = 5²× 17¹
30 = 1 × 2 × 3 × 5 = 2¹ × 3¹× 5¹
HCF of 1050, 750, and 425 = 5² = 25
Hence, the length of the longest tape which can measure the three dimensions of the room exactly is 25 cm

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