Question

What is the maximum value of HCF of $[n^2+17]$ and $(n+1{)}^2+17]?$

• A. 69
• B. 85
• C. 170
• D. None of these

Answer 1

The correct option is A 69

HCF(n² + 17, (n + 1)² + 17)
= HCF(n² + 17, {(n + 1)² + 17} - {n² + 17})
= HCF(n² + 17, 2n + 1) = HCF(2{n² + 17}, 2n + 1)
= HCF(2{n² + 17} - n{2n + 1}, 2n + 1)
= HCF(34 - n, 2n + 1)
= HCF(2{34 - n} + {2n + 1}, 2n + 1)
= HCF(69, 2n + 1) = 69 if 2n + 1 is divisible by 69.