What are the divisors of 1119?

1, 3, 373, 1119

There is a total of 4 positive divisors.
The sum of these divisors is 1496.
The arithmetic mean is 374.

4 odd divisors

1, 3, 373, 1119

How to compute the divisors of 1119?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 1119 by each of the numbers from 1 to 1119 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

1119 / 1 = 1119 (the remainder is 0, so 1 is a divisor of 1119)
1119 / 2 = 559.5 (the remainder is 1, so 2 is not a divisor of 1119)
1119 / 3 = 373 (the remainder is 0, so 3 is a divisor of 1119)
...
1119 / 1118 = 1.0008944543828 (the remainder is 1, so 1118 is not a divisor of 1119)
1119 / 1119 = 1 (the remainder is 0, so 1119 is a divisor of 1119)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 1119 (i.e. 33.451457367355). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

1119 / 1 = 1119 (the remainder is 0, so 1 and 1119 are divisors of 1119)
1119 / 2 = 559.5 (the remainder is 1, so 2 is not a divisor of 1119)
1119 / 3 = 373 (the remainder is 0, so 3 and 373 are divisors of 1119)
...
1119 / 32 = 34.96875 (the remainder is 31, so 32 is not a divisor of 1119)
1119 / 33 = 33.909090909091 (the remainder is 30, so 33 is not a divisor of 1119)