6561

6561 is an integer in decimal notation. It equals 3^8, and can also be written as 9^4 and 81^2. This makes it a perfect square and a perfect fourth power, as well as an eighth power of 3.

Prime factorization and divisors: 6561 = 3^8. Consequently, its positive divisors are 1, 3, 9, 27, 81, 243, 729, 2187, and 6561, totaling nine divisors.

Base representations and digit properties: In base 3, 6561 is 100000000_3; in base 9, it is 10000_9; in base 81, it is 100_81. In decimal, the sum of digits is 18, so the number is divisible by 9 and by 3; the digital root is 9.

Context and significance: Because 6561 is a pure power of 3, it serves as a straightforward example of a number that is simultaneously a square, a fourth power, and an eighth power. Its multiple representations across bases that are powers of 3 illustrate how powers of a base manifest as simple forms in complementary bases. As a member of the sequence of powers of 3, 6561 appears in various mathematical discussions related to exponentiation, base conversion, and the structure of perfect powers.