A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?

Question

Accepted Answer

4. The bottle size must be a common divisor of 399 and 532. 399 = 3 × 7 × 19, and 532 = 2² × 7 × 19. GCD(399, 532) = 7 × 19 = 133. Divisors of 133 are 1, 7, 19, 133 — that is 4 different bottle sizes.

A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?

Explanation

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