1253 is a natural number that follows 1252 and precedes 1254. In elementary arithmetic it is an odd, positive integer with a small, easily described factorization: 1253 = 7 × 179. Because it is the product of exactly two primes, 1253 is classified as a semiprime and is squarefree (no repeated prime factors).
Mathematical properties
- Prime factorization: 7 × 179.
- Divisors: 1, 7, 179, 1253 (four divisors in total).
- Sum of divisors (σ): 1 + 7 + 179 + 1253 = 1440.
- Euler's totient φ(1253) = (7 − 1)(179 − 1) = 6 × 178 = 1068.
- Digit sum (base 10): 1 + 2 + 5 + 3 = 11.
- Parity and shape: odd, non-palindromic, not a perfect power.
Representations and notation
In common positional systems 1253 appears as follows: binary 10011100101, octal 2345, and hexadecimal 0x4E5. In Roman numerals it is written MCCLIII. As an ordinal it is spoken as "one thousand two hundred fifty-third" (1253rd).
Because of its simple factorization, 1253 is used in elementary number-theory examples that illustrate semiprimes, totients, and divisor functions. It also appears as a numeric label in catalogs, model numbers, and dates: for instance, 1253 can denote the calendar year AD 1253 or 1253 BC in historical chronologies. When treated purely as an integer, it serves as a typical small composite for exercises in primality testing and modular arithmetic.
Notable distinctions: 1253 is not prime but is the product of two distinct primes, which makes many multiplicative-arithmetic functions easy to compute. Its small set of divisors and moderate totient value make it convenient for classroom demonstrations of the relationships among factorization, divisors and Euler's function.