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The remainder when a number 2851 × (2862)2 × (2873)3 is divided by 23, is:
1. 5
2. 17
3. 18
4. 19

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Correct Answer - Option 3 : 18

Given :

The remainder when a number 2851 × (2862) × (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

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