What are the divisors of 5872?

1, 2, 4, 8, 16, 367, 734, 1468, 2936, 5872

There is a total of 10 positive divisors.
The sum of these divisors is 11408.
The arithmetic mean is 1140.8.

8 even divisors

2, 4, 8, 16, 734, 1468, 2936, 5872

2 odd divisors

1, 367

How to compute the divisors of 5872?

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 5872 by each of the numbers from 1 to 5872 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)

5872 / 1 = 5872 (the remainder is 0, so 1 is a divisor of 5872)
5872 / 2 = 2936 (the remainder is 0, so 2 is a divisor of 5872)
5872 / 3 = 1957.3333333333 (the remainder is 1, so 3 is not a divisor of 5872)
...
5872 / 5871 = 1.0001703287345 (the remainder is 1, so 5871 is not a divisor of 5872)
5872 / 5872 = 1 (the remainder is 0, so 5872 is a divisor of 5872)

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 5872 (i.e. 76.628976242672). 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 $\frac{N}{d} = D$ )

5872 / 1 = 5872 (the remainder is 0, so 1 and 5872 are divisors of 5872)
5872 / 2 = 2936 (the remainder is 0, so 2 and 2936 are divisors of 5872)
5872 / 3 = 1957.3333333333 (the remainder is 1, so 3 is not a divisor of 5872)
...
5872 / 75 = 78.293333333333 (the remainder is 22, so 75 is not a divisor of 5872)
5872 / 76 = 77.263157894737 (the remainder is 20, so 76 is not a divisor of 5872)