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What is the largest number that divides 245 and 1029, leaving remainder 5 in each case? (a) 15 (b) 16 (c) 9 (d) 5

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What is the largest number that divides 245 and 1029, leaving remainder 5 in each case? 

(a) 15 (b) 16 (c) 9 (d) 5

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(b) 16 

We know that the required number divides 240 (245 – 5) and 1024 (1029 – 5). 

∴ Required number = HCF (240, 1024) 

240 = 2 × 2 × 2 × 2 × 3 × 5 

1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 

∴ HCF = 2 × 2 × 2 × 2 = 16

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