If \(525 \equiv (10 + K) \pmod{7}\) where \(K \in \mathrm{N}\), then the least value of K is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
\(a \equiv b \pmod{7}\) means that 7 divides a − b, that is, a and b leave the same remainder on division by 7.
\(525 = 7 \times 75\), so \(525 \equiv 0 \pmod{7}\)
So 10 + K must be a multiple of 7. The smallest multiple of 7 above 10 is 14:
\(10 + K = 14\)
\(K = 4\)
So the least natural number K is 4.