A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in…
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?
3
4
5
6
Solution
The bottle size must divide both 399 and 532. $399 = 3 \times 7 \times 19$ and $532 = 2^2 \times 7 \times 19$. Their HCF is $7 \times 19 = 133$. The common divisors are 1, 7, 19 and 133 - that is 4 possible bottle sizes.