3577

3577 is a natural number that sits between 3576 and 3578. In arithmetic, it has the prime factorization 3577 = 7^2 × 73, making it a composite number. It has exactly six positive divisors: 1, 7, 49, 73, 511, and 3577. The number is odd and congruent to 1 modulo 4.

Because every prime congruent to 3 mod 4 occurs with an even exponent in its factorization, 3577 can be expressed as a sum of two squares. One valid representation is 3577 = 56^2 + 21^2. This can also be seen by noting that 73 = 8^2 + 3^2 and multiplying by 7^2 yields (7×8)^2 + (7×3)^2.

In common numeral systems, 3577 is written as 0xDF9 in hexadecimal and as 110111111001 in binary. In base 7, the value is 13300_7.

Summary: 3577 is a composite number with factorization 7^2 × 73, has six divisors, is odd and ≡ 1 (mod 4), and can be represented as a sum of two squares (56^2 + 21^2). It serves as an example in number theory of how prime factors influence representations of a number as a sum of two squares.