The remainder when 1010 ⋅ (1010 + 1) (1010 + 2) is divided by 6 is

Question

The remainder when 1010 ⋅ (1010 + 1) (1010 + 2) is divided by 6 is (A) 2 (B) 4 (C) 0 (D) 6

Tardigrade Admin · Accepted Answer

Here, 1010 ⋅(1010+1) ⋅(1010+2) is a product of 3 consecutive integers. Therefore, it is divisible by 3 ! i.e., 6 . So, required remainder is 0

Q. The remainder when $1 0^{10} \cdot (1 0^{10} + 1) (1 0^{10} + 2)$ is divided by $6$ is