State which of the following statement is true 2^ 16 −1 is divisi… - Vidyadip

MCQ

State which of the following statement is true $2^{16} −1$ is divisibleby:

A
$11$
B
$13$
✓
$17$
D
$19$

✓

Answer

Correct option: C.

$17$

$2^{16} – 1 = 65536 – 1 = 65535$
$= 3 × 5 × 17 × 257$
Hence, $2^{16} – 1$ is divisible by $17$

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