What are the divisors of 8252?

1, 2, 4, 2063, 4126, 8252

There is a total of 6 positive divisors.
The sum of these divisors is 14448.
The arithmetic mean is 2408.

4 even divisors

2, 4, 4126, 8252

2 odd divisors

1, 2063

How to compute the divisors of 8252?

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 8252 by each of the numbers from 1 to 8252 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)

8252 / 1 = 8252 (the remainder is 0, so 1 is a divisor of 8252)
8252 / 2 = 4126 (the remainder is 0, so 2 is a divisor of 8252)
8252 / 3 = 2750.6666666667 (the remainder is 2, so 3 is not a divisor of 8252)
...
8252 / 8251 = 1.0001211974306 (the remainder is 1, so 8251 is not a divisor of 8252)
8252 / 8252 = 1 (the remainder is 0, so 8252 is a divisor of 8252)

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 8252 (i.e. 90.840519593406). 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 $\frac{N}{d} = D$ )

8252 / 1 = 8252 (the remainder is 0, so 1 and 8252 are divisors of 8252)
8252 / 2 = 4126 (the remainder is 0, so 2 and 4126 are divisors of 8252)
8252 / 3 = 2750.6666666667 (the remainder is 2, so 3 is not a divisor of 8252)
...
8252 / 89 = 92.719101123596 (the remainder is 64, so 89 is not a divisor of 8252)
8252 / 90 = 91.688888888889 (the remainder is 62, so 90 is not a divisor of 8252)