What are the divisors of 4652?

1, 2, 4, 1163, 2326, 4652

There is a total of 6 positive divisors.
The sum of these divisors is 8148.
The arithmetic mean is 1358.

4 even divisors

2, 4, 2326, 4652

2 odd divisors

1, 1163

How to compute the divisors of 4652?

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 4652 by each of the numbers from 1 to 4652 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)

4652 / 1 = 4652 (the remainder is 0, so 1 is a divisor of 4652)
4652 / 2 = 2326 (the remainder is 0, so 2 is a divisor of 4652)
4652 / 3 = 1550.6666666667 (the remainder is 2, so 3 is not a divisor of 4652)
...
4652 / 4651 = 1.0002150075253 (the remainder is 1, so 4651 is not a divisor of 4652)
4652 / 4652 = 1 (the remainder is 0, so 4652 is a divisor of 4652)

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 4652 (i.e. 68.20557161992). 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 $\frac{N}{d} = D$ )

4652 / 1 = 4652 (the remainder is 0, so 1 and 4652 are divisors of 4652)
4652 / 2 = 2326 (the remainder is 0, so 2 and 2326 are divisors of 4652)
4652 / 3 = 1550.6666666667 (the remainder is 2, so 3 is not a divisor of 4652)
...
4652 / 67 = 69.432835820896 (the remainder is 29, so 67 is not a divisor of 4652)
4652 / 68 = 68.411764705882 (the remainder is 28, so 68 is not a divisor of 4652)