MCQ
Let $N_1=2^{55}+1$ and $N_2=165$.Then
- A$N_1$ and $N_2$ are coprime
- Bthe $HCF$ (Highest Common Factor) of $N_1$ and $N_2$ is $55$
- Cthe $HCF$ of $N_1$ and $N_2$ is $11$
- ✓the $HCF$ of $N_1$ and $N_2$ is $33$
It is given that, $N_2=165$ $=3 \times 5 \times 11$ and $N_1=2^{55}+1$
As we know that, if $n$ is odd integer then $x^n+y^n$ is divisible by $x+y$.
So, $N_1=2^{55}+1^{55}$ is divisible by $2+1=3$ and $N_1=2^{55}+1^{55}$
$=\left(2^5\right)^{11}+\left(1^5\right)^{11}=(32)^{11}+(1)^{11}$
is divisible by $32+1=33$
$\therefore$ the HCF of $N_1$ and $N_2$ is $33$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.