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Largest number which divides 145, 325 and 415 to leave the same remainder in each case is:

Largest number which divides 145, 325 and 415 to leave the same remainder in each case is: Correct Answer 90

Concept:

The greatest number that will divide a, b and c leaving the same remainder in each case is given by = HCF of (a – b), (b – c), (c – a)

Calculation:

HCF of (325 – 145), (415 – 325), (415 – 145)

HCF of 180, 90, 270

180 = 2 × 2 × 3 × 3 × 5

90 = 2 × 3 × 3 × 5

270 = 2 × 3 × 3 × 3 × 5

∴ HCF of 180, 90 and 270 = 2 × 3 × 3 × 5 = 90

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