Correct Answer - Option 3 : 18
Given :
The remainder when a number 2851 × (2862)2 × (2873)3 is divided by 23, is = ?
Formula used :
Using basic modular arithmetic :
xa yb zc = (xa mod m) (yb mod m) (zc mod m)
mod equal to multiple of m.
Calculation
⇒ 2851 = 22(mod 23) = - 1 mod 23
⇒ 28622 =(2862 mod 23)2 mod 23 = (10 mod 23)2 mod 23 = 8 mod 23
⇒ 28733 = (2873 mod 23)3 mod 23 = (-2 mod 23)3 mod 23 = -8 mod 23
⇒ -1 × 8 × -8 mod 23 = 64 mod 23 = 18
∴ The required answer is 18