Overview
1125 is an integer that lies between 1124 and 1126. As a counting number it appears in arithmetic, calendrical designations, product model numbers and other enumerations. Mathematically it is notable for a compact prime factorization and several elementary divisor and totient properties.
Mathematical characteristics
The prime factorization of 1125 is 3^2 × 5^3. From this follow many consequences: it has (2+1)×(3+1)=12 positive divisors, its Euler totient is φ(1125)=1125×(1−1/3)×(1−1/5)=600, and the sum of all divisors σ(1125)=2028. The sum of proper divisors is 2028−1125=903, so 1125 is a deficient number (proper divisor sum less than the number).
Divisors and basic arithmetic
All positive divisors are generated by choosing powers of 3 (0–2) and 5 (0–3). They are:
- 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125
1125 factors nicely as 45×25 and as 9×125; it is divisible by 3, 5, 9, 25 and 125. It is not a perfect power (the exponents 2 and 3 have gcd 1), and it is a Harshad number in base 10 because the sum of its digits (1+1+2+5=9) divides it evenly (1125/9=125).
Representations and congruences
In binary 1125 is written 10001100101, in octal 2145 and in hexadecimal 0x465. Because its prime factors are 3 and 5 it satisfies simple congruences modulo small bases (for example, divisible by 9 and by 25). Its Euler totient 600 means there are 600 integers less than 1125 that are coprime to it.
Year and other uses
As a year number, "1125" refers to the twelfth-century AD (Common Era) year 1125. In modern contexts the sequence 1125 also serves as a model, product, route, or document number; those applications are conventional labels rather than mathematical meanings.