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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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
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 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 + 155 is 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.