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 :

x^{a} y^{b} z^{c} = (x^{a} mod m) (y^{b} mod m) (z^{c} mod m)

mod equal to multiple of m.

**Calculation**

⇒ 2851 = 22(mod 23) = - 1 mod 23

⇒ 2862^{2} =(2862 mod 23)^{2} mod 23 = (10 mod 23)^{2} mod 23 = 8 mod 23

⇒ 2873^{3} = (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**