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A vendor has 3 kinds of shakes i.e. chocolate, strawberry and banana. He has 204 litres of chocolate shake, 170 litres of strawberry shake and 374 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?

A vendor has 3 kinds of shakes i.e. chocolate, strawberry and banana. He has 204 litres of chocolate shake, 170 litres of strawberry shake and 374 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? Correct Answer 4

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 204, 170 and 374

204 = 34 × 2 × 3

170 = 34 × 5

374 = 34 × 11

⇒ H.C.F. = 34

Factors of 34 = 1, 2, 17, 34

⇒ Size of bottles = 1, 2, 17, 34

∴ Options for sizes are 4

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