What are the divisors of 1141?

1, 7, 163, 1141

There is a total of 4 positive divisors.
The sum of these divisors is 1312.
The arithmetic mean is 328.

4 odd divisors

1, 7, 163, 1141

How to compute the divisors of 1141?

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 1141 by each of the numbers from 1 to 1141 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)

1141 / 1 = 1141 (the remainder is 0, so 1 is a divisor of 1141)
1141 / 2 = 570.5 (the remainder is 1, so 2 is not a divisor of 1141)
1141 / 3 = 380.33333333333 (the remainder is 1, so 3 is not a divisor of 1141)
...
1141 / 1140 = 1.0008771929825 (the remainder is 1, so 1140 is not a divisor of 1141)
1141 / 1141 = 1 (the remainder is 0, so 1141 is a divisor of 1141)

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 1141 (i.e. 33.778691508109). 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 $\frac{N}{d} = D$ )

1141 / 1 = 1141 (the remainder is 0, so 1 and 1141 are divisors of 1141)
1141 / 2 = 570.5 (the remainder is 1, so 2 is not a divisor of 1141)
1141 / 3 = 380.33333333333 (the remainder is 1, so 3 is not a divisor of 1141)
...
1141 / 32 = 35.65625 (the remainder is 21, so 32 is not a divisor of 1141)
1141 / 33 = 34.575757575758 (the remainder is 19, so 33 is not a divisor of 1141)