What are the divisors of 1137?

1, 3, 379, 1137

There is a total of 4 positive divisors.
The sum of these divisors is 1520.
The arithmetic mean is 380.

4 odd divisors

1, 3, 379, 1137

How to compute the divisors of 1137?

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 1137 by each of the numbers from 1 to 1137 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)

1137 / 1 = 1137 (the remainder is 0, so 1 is a divisor of 1137)
1137 / 2 = 568.5 (the remainder is 1, so 2 is not a divisor of 1137)
1137 / 3 = 379 (the remainder is 0, so 3 is a divisor of 1137)
...
1137 / 1136 = 1.0008802816901 (the remainder is 1, so 1136 is not a divisor of 1137)
1137 / 1137 = 1 (the remainder is 0, so 1137 is a divisor of 1137)

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 1137 (i.e. 33.719430600175). 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 $\frac{N}{d} = D$ )

1137 / 1 = 1137 (the remainder is 0, so 1 and 1137 are divisors of 1137)
1137 / 2 = 568.5 (the remainder is 1, so 2 is not a divisor of 1137)
1137 / 3 = 379 (the remainder is 0, so 3 and 379 are divisors of 1137)
...
1137 / 32 = 35.53125 (the remainder is 17, so 32 is not a divisor of 1137)
1137 / 33 = 34.454545454545 (the remainder is 15, so 33 is not a divisor of 1137)