What are the divisors of 5852?

1, 2, 4, 7, 11, 14, 19, 22, 28, 38, 44, 76, 77, 133, 154, 209, 266, 308, 418, 532, 836, 1463, 2926, 5852

There is a total of 24 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 560.

16 even divisors

2, 4, 14, 22, 28, 38, 44, 76, 154, 266, 308, 418, 532, 836, 2926, 5852

8 odd divisors

1, 7, 11, 19, 77, 133, 209, 1463

How to compute the divisors of 5852?

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 5852 by each of the numbers from 1 to 5852 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)

5852 / 1 = 5852 (the remainder is 0, so 1 is a divisor of 5852)
5852 / 2 = 2926 (the remainder is 0, so 2 is a divisor of 5852)
5852 / 3 = 1950.6666666667 (the remainder is 2, so 3 is not a divisor of 5852)
...
5852 / 5851 = 1.0001709109554 (the remainder is 1, so 5851 is not a divisor of 5852)
5852 / 5852 = 1 (the remainder is 0, so 5852 is a divisor of 5852)

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 5852 (i.e. 76.498365995621). 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 $\frac{N}{d} = D$ )

5852 / 1 = 5852 (the remainder is 0, so 1 and 5852 are divisors of 5852)
5852 / 2 = 2926 (the remainder is 0, so 2 and 2926 are divisors of 5852)
5852 / 3 = 1950.6666666667 (the remainder is 2, so 3 is not a divisor of 5852)
...
5852 / 75 = 78.026666666667 (the remainder is 2, so 75 is not a divisor of 5852)
5852 / 76 = 77 (the remainder is 0, so 76 and 77 are divisors of 5852)