What are the divisors of 2852?

1, 2, 4, 23, 31, 46, 62, 92, 124, 713, 1426, 2852

There is a total of 12 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 448.

8 even divisors

2, 4, 46, 62, 92, 124, 1426, 2852

4 odd divisors

1, 23, 31, 713

How to compute the divisors of 2852?

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 2852 by each of the numbers from 1 to 2852 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)

2852 / 1 = 2852 (the remainder is 0, so 1 is a divisor of 2852)
2852 / 2 = 1426 (the remainder is 0, so 2 is a divisor of 2852)
2852 / 3 = 950.66666666667 (the remainder is 2, so 3 is not a divisor of 2852)
...
2852 / 2851 = 1.0003507541214 (the remainder is 1, so 2851 is not a divisor of 2852)
2852 / 2852 = 1 (the remainder is 0, so 2852 is a divisor of 2852)

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 2852 (i.e. 53.404119691275). 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 $\frac{N}{d} = D$ )

2852 / 1 = 2852 (the remainder is 0, so 1 and 2852 are divisors of 2852)
2852 / 2 = 1426 (the remainder is 0, so 2 and 1426 are divisors of 2852)
2852 / 3 = 950.66666666667 (the remainder is 2, so 3 is not a divisor of 2852)
...
2852 / 52 = 54.846153846154 (the remainder is 44, so 52 is not a divisor of 2852)
2852 / 53 = 53.811320754717 (the remainder is 43, so 53 is not a divisor of 2852)