Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times.
To solve this problem, we need to find the greatest common divisor (GCD) of the three given quantities: 403 litres, 434 litres, and 465 litres.
The GCD will be the maximum capacity of a container that can measure all three amounts an exact number of times.
Find the GCD of 403, 434, and 465
Step 1: GCD of 403 and 434
Use the Euclidean algorithm:
434 ÷ 403 = 1 remainder 31
403 ÷ 31 = 13 remainder 0
So, GCD(403, 434) = 31
Step2: Now, GCD 31 and 465
465 ÷ 31 = 15 remainder 0
So, GCD(31, 465) = 31
Hence the maximum capacity of the container that can measure all three diesel quantities exactly is 31 litres.
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