UPSC CDS Math Number System Questions

Remainder when $4444^1$ is divided by 9 = 7Remainder when $4444^2$ is divided by 9 = 4Remainder when $4444^3$ is divided by 9 = 1Remainder when $4444^4$ is divided by 9 = 7Remainder when $4444^5$ is divided by 9 = 4Remainder when $4444^6$ is divided by 9 = 1, and so onNow, Remainder when $4444^{3\times 1481}$ is divided by 9 = 1Therefore, remainder when $4444^{3\times 1481}\times 4444$ is divided by 9 = Remainder when 4444 is divided by 9 = 7. Thus, the remainder when $4444^{4444}$ is divided by 9 is 7.