Let N1 = 255 + 1 and N2 = 165.Then(a) N1 and N2 are co-prime(b) the

1.	Let N1 = 255 + 1 and N2 = 165.Then(a) N1 and N2 are co-prime(b) the HCF (Highest Common Factor) of N1 and N2 is 55(c) the HCF of N1 and N2 is 11(d) the HCF of N1 and N2 is 33
Answer» Answer is : (d) the HCF of N₁ and N₂ is 33 It is given that, N₂ = 165 = 3 x 5 x 11 and N₁ = 2⁵⁵ + 1 As we know that, if n is odd integer then xⁿ + yⁿ is divisible by x + y. So, N₁ = 2⁵⁵+ 1⁵⁵is divisible by 2 + 1 = 3 and N₁ = 2⁵⁵ + 1⁵⁵ = (2⁵)¹¹+ (1⁵)¹¹ = (32)¹¹+ (1)¹¹ is divisible by 32 + 1 = 33 ∴ the HCF of N₁ and N₂ is 33.

Let N1 = 255 + 1 and N2 = 165.Then(a) N1 and N2 are co-prime(b) the HCF (Highest Common Factor) of N1 and N2 is 55(c) the HCF of N1 and N2 is 11(d) the HCF of N1 and N2 is 33

Answer»

Answer is : (d) the HCF of N₁ and N₂ is 33

It is given that, N₂ = 165

= 3 x 5 x 11 and N₁ = 2⁵⁵ + 1

As we know that, if n is odd integer then xⁿ + yⁿ is divisible by x + y.

So, N₁ = 2⁵⁵+ 1⁵⁵is divisible by 2 + 1 = 3 and N₁ = 2⁵⁵ + 1⁵⁵

= (2⁵)¹¹+ (1⁵)¹¹ = (32)¹¹+ (1)¹¹

is divisible by 32 + 1 = 33

∴ the HCF of N₁ and N₂ is 33.

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Let N1 = 255 + 1 and N2 = 165.Then(a) N1 and N2 are co-prime(b) the HCF (Highest Common Factor) of N1 and N2 is 55(c) the HCF of N1 and N2 is 11(d) the HCF of N1 and N2 is 33

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