What are the divisors of 4592?

1, 2, 4, 7, 8, 14, 16, 28, 41, 56, 82, 112, 164, 287, 328, 574, 656, 1148, 2296, 4592

There is a total of 20 positive divisors.
The sum of these divisors is 10416.
The arithmetic mean is 520.8.

16 even divisors

2, 4, 8, 14, 16, 28, 56, 82, 112, 164, 328, 574, 656, 1148, 2296, 4592

4 odd divisors

1, 7, 41, 287

How to compute the divisors of 4592?

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 4592 by each of the numbers from 1 to 4592 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)

4592 / 1 = 4592 (the remainder is 0, so 1 is a divisor of 4592)
4592 / 2 = 2296 (the remainder is 0, so 2 is a divisor of 4592)
4592 / 3 = 1530.6666666667 (the remainder is 2, so 3 is not a divisor of 4592)
...
4592 / 4591 = 1.000217817469 (the remainder is 1, so 4591 is not a divisor of 4592)
4592 / 4592 = 1 (the remainder is 0, so 4592 is a divisor of 4592)

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 4592 (i.e. 67.76429738439). 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 $\frac{N}{d} = D$ )

4592 / 1 = 4592 (the remainder is 0, so 1 and 4592 are divisors of 4592)
4592 / 2 = 2296 (the remainder is 0, so 2 and 2296 are divisors of 4592)
4592 / 3 = 1530.6666666667 (the remainder is 2, so 3 is not a divisor of 4592)
...
4592 / 66 = 69.575757575758 (the remainder is 38, so 66 is not a divisor of 4592)
4592 / 67 = 68.537313432836 (the remainder is 36, so 67 is not a divisor of 4592)