What are the divisors of 5888?

1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 128, 184, 256, 368, 736, 1472, 2944, 5888

There is a total of 18 positive divisors.
The sum of these divisors is 12264.
The arithmetic mean is 681.33333333333.

16 even divisors

2, 4, 8, 16, 32, 46, 64, 92, 128, 184, 256, 368, 736, 1472, 2944, 5888

2 odd divisors

1, 23

How to compute the divisors of 5888?

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 5888 by each of the numbers from 1 to 5888 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)

5888 / 1 = 5888 (the remainder is 0, so 1 is a divisor of 5888)
5888 / 2 = 2944 (the remainder is 0, so 2 is a divisor of 5888)
5888 / 3 = 1962.6666666667 (the remainder is 2, so 3 is not a divisor of 5888)
...
5888 / 5887 = 1.000169865806 (the remainder is 1, so 5887 is not a divisor of 5888)
5888 / 5888 = 1 (the remainder is 0, so 5888 is a divisor of 5888)

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 5888 (i.e. 76.733304373004). 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 $\frac{N}{d} = D$ )

5888 / 1 = 5888 (the remainder is 0, so 1 and 5888 are divisors of 5888)
5888 / 2 = 2944 (the remainder is 0, so 2 and 2944 are divisors of 5888)
5888 / 3 = 1962.6666666667 (the remainder is 2, so 3 is not a divisor of 5888)
...
5888 / 75 = 78.506666666667 (the remainder is 38, so 75 is not a divisor of 5888)
5888 / 76 = 77.473684210526 (the remainder is 36, so 76 is not a divisor of 5888)