What are the divisors of 5144?

1, 2, 4, 8, 643, 1286, 2572, 5144

There is a total of 8 positive divisors.
The sum of these divisors is 9660.
The arithmetic mean is 1207.5.

6 even divisors

2, 4, 8, 1286, 2572, 5144

2 odd divisors

1, 643

How to compute the divisors of 5144?

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 5144 by each of the numbers from 1 to 5144 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)

5144 / 1 = 5144 (the remainder is 0, so 1 is a divisor of 5144)
5144 / 2 = 2572 (the remainder is 0, so 2 is a divisor of 5144)
5144 / 3 = 1714.6666666667 (the remainder is 2, so 3 is not a divisor of 5144)
...
5144 / 5143 = 1.0001944390434 (the remainder is 1, so 5143 is not a divisor of 5144)
5144 / 5144 = 1 (the remainder is 0, so 5144 is a divisor of 5144)

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 5144 (i.e. 71.721684308164). 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 $\frac{N}{d} = D$ )

5144 / 1 = 5144 (the remainder is 0, so 1 and 5144 are divisors of 5144)
5144 / 2 = 2572 (the remainder is 0, so 2 and 2572 are divisors of 5144)
5144 / 3 = 1714.6666666667 (the remainder is 2, so 3 is not a divisor of 5144)
...
5144 / 70 = 73.485714285714 (the remainder is 34, so 70 is not a divisor of 5144)
5144 / 71 = 72.450704225352 (the remainder is 32, so 71 is not a divisor of 5144)