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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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