If $525 ≡(10+ K) (mod\, 7)$ where $K ∈ N$, then the least value of K is:

4

The correct answer is Option (2) → 4

$525 \equiv (10 + K) \pmod{7}$

Compute $525 \mod 7$ : $525 \div 7 = 75$ remainder $0 \Rightarrow 525 \equiv 0 \pmod{7}$

Compute $10 \mod 7$: $10 \equiv 3 \pmod{7}$

Then $10 + K \equiv 3 + K \equiv 0 \pmod{7} \Rightarrow K \equiv -3 \equiv 4 \pmod{7}$

Least value of $K = 4$