What are the divisors of 1144?

1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572, 1144

There is a total of 16 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 157.5.

12 even divisors

2, 4, 8, 22, 26, 44, 52, 88, 104, 286, 572, 1144

4 odd divisors

1, 11, 13, 143

How to compute the divisors of 1144?

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 1144 by each of the numbers from 1 to 1144 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)

1144 / 1 = 1144 (the remainder is 0, so 1 is a divisor of 1144)
1144 / 2 = 572 (the remainder is 0, so 2 is a divisor of 1144)
1144 / 3 = 381.33333333333 (the remainder is 1, so 3 is not a divisor of 1144)
...
1144 / 1143 = 1.0008748906387 (the remainder is 1, so 1143 is not a divisor of 1144)
1144 / 1144 = 1 (the remainder is 0, so 1144 is a divisor of 1144)

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 1144 (i.e. 33.823069050576). 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 $\frac{N}{d} = D$ )

1144 / 1 = 1144 (the remainder is 0, so 1 and 1144 are divisors of 1144)
1144 / 2 = 572 (the remainder is 0, so 2 and 572 are divisors of 1144)
1144 / 3 = 381.33333333333 (the remainder is 1, so 3 is not a divisor of 1144)
...
1144 / 32 = 35.75 (the remainder is 24, so 32 is not a divisor of 1144)
1144 / 33 = 34.666666666667 (the remainder is 22, so 33 is not a divisor of 1144)