Three tankers contain 403 lltres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of three containers exact number of times.

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Solution

The maximum capacity of three containers is equal to the HCF of 403, 434 and 465.
403 = 1 × 13 × 31 = 13¹ × 31¹
434 = 1 × 2 × 7 × 31 = 2¹ × 7¹ × 31¹
465 = 1 × 3 × 5 × 31 = 3¹ × 5¹ × 31¹
HCF of 403, 434 and 465 = 31¹ = 31
Hence, the maximum capacity of a container that can measure the diesel of three containers exact number of times is 31 litres

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