What are the divisors of 5052?

1, 2, 3, 4, 6, 12, 421, 842, 1263, 1684, 2526, 5052

There is a total of 12 positive divisors.
The sum of these divisors is 11816.
The arithmetic mean is 984.66666666667.

8 even divisors

2, 4, 6, 12, 842, 1684, 2526, 5052

4 odd divisors

1, 3, 421, 1263

How to compute the divisors of 5052?

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 5052 by each of the numbers from 1 to 5052 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)

5052 / 1 = 5052 (the remainder is 0, so 1 is a divisor of 5052)
5052 / 2 = 2526 (the remainder is 0, so 2 is a divisor of 5052)
5052 / 3 = 1684 (the remainder is 0, so 3 is a divisor of 5052)
...
5052 / 5051 = 1.0001979805979 (the remainder is 1, so 5051 is not a divisor of 5052)
5052 / 5052 = 1 (the remainder is 0, so 5052 is a divisor of 5052)

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 5052 (i.e. 71.077422575667). 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 $\frac{N}{d} = D$ )

5052 / 1 = 5052 (the remainder is 0, so 1 and 5052 are divisors of 5052)
5052 / 2 = 2526 (the remainder is 0, so 2 and 2526 are divisors of 5052)
5052 / 3 = 1684 (the remainder is 0, so 3 and 1684 are divisors of 5052)
...
5052 / 70 = 72.171428571429 (the remainder is 12, so 70 is not a divisor of 5052)
5052 / 71 = 71.154929577465 (the remainder is 11, so 71 is not a divisor of 5052)