A vendor has 3 kinds of shakes i.e. chocolate, strawberry and banana. He has 180 litres of chocolate shake, 360 litres of strawberry shake and 540 litres of banana shake. He wants to bottle them in bottles of equal sizes – such that each of the variety is bottled completely. How many options for the size of bottle does the vendor have?
The number of bottle sizes can be given by taking out factors of the H.C.F. of the quantity of 3 varieties ⇒ H.C.F. of 180, 360 and 540 180 = 2 × 2 × 3 × 3 × 5 360 = 2 × 2 × 2 × 3 × 3 × 5 540 = 2 × 2 × 3 × 3 × 3 × 5 ⇒ H.C.F. = 180 Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180 ⇒ Size of bottles = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180 ∴ Options for sizes are 18
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