8. The length, breadth and height of a room are 762 cm, 576 cm and 332 cm respectively. Find the
longest tape which can measure the three dimensions of the room exactly
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Step-by-step explanation:
Given,
Length = 825cm
Breadth = 675cm
Height = 450cm
We should find the HCF of 825,675 and 450 to find the longest tape.
Prime Factorisation of 450 =
Prime Factorisation of 675 =
Prime Factorisation of 875 =
Thus,
450 = 2 × 3 × 3 × 3 × 5 × 5
675 = 3 × 3 × 3 × 5 × 5
875 = 3 × 5 × 5 × 11
Above, 3, 5 and 5 are common factors.
Hence, 3 × 5 × 5 = 75
Therefore, the measure of longest tape is 75cm.
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