What are the divisors of 4144?

1, 2, 4, 7, 8, 14, 16, 28, 37, 56, 74, 112, 148, 259, 296, 518, 592, 1036, 2072, 4144

There is a total of 20 positive divisors.
The sum of these divisors is 9424.
The arithmetic mean is 471.2.

16 even divisors

2, 4, 8, 14, 16, 28, 56, 74, 112, 148, 296, 518, 592, 1036, 2072, 4144

4 odd divisors

1, 7, 37, 259

How to compute the divisors of 4144?

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 4144 by each of the numbers from 1 to 4144 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)

4144 / 1 = 4144 (the remainder is 0, so 1 is a divisor of 4144)
4144 / 2 = 2072 (the remainder is 0, so 2 is a divisor of 4144)
4144 / 3 = 1381.3333333333 (the remainder is 1, so 3 is not a divisor of 4144)
...
4144 / 4143 = 1.0002413709872 (the remainder is 1, so 4143 is not a divisor of 4144)
4144 / 4144 = 1 (the remainder is 0, so 4144 is a divisor of 4144)

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 4144 (i.e. 64.373907757724). 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 $\frac{N}{d} = D$ )

4144 / 1 = 4144 (the remainder is 0, so 1 and 4144 are divisors of 4144)
4144 / 2 = 2072 (the remainder is 0, so 2 and 2072 are divisors of 4144)
4144 / 3 = 1381.3333333333 (the remainder is 1, so 3 is not a divisor of 4144)
...
4144 / 63 = 65.777777777778 (the remainder is 49, so 63 is not a divisor of 4144)
4144 / 64 = 64.75 (the remainder is 48, so 64 is not a divisor of 4144)