513

513 is a natural number that follows 512 and precedes 514. In mathematics it is an odd composite number with prime factorization 3^3 × 19.

Its divisors are 1, 3, 9, 19, 27, 57, 171, and 513. Because the sum of its digits is 9, 513 is divisible by 9, making it a Harshad number in base 10 (513 ÷ 9 = 57). The number is also expressible as a sum of two consecutive integers: 256 + 257 = 513.

In numeral systems, 513 is written as 1000000001 in binary, 0x201 in hexadecimal, and 1001 in octal. This reflects that 2^9 = 512, so 513 equals 2^9 + 1.

In telecommunications, 513 is the area code for Cincinnati and surrounding areas in southwestern Ohio. It was created in 1947 as one of the original area codes under the North American Numbering Plan and remains in use for its region.

Culturally, 513 is primarily encountered as a mathematical and practical identifier rather than a number with widely recognized symbolic meaning. It appears in contexts such as mathematics education, computer representations, and regional dialing plans.

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