What are the divisors of 5612?

1, 2, 4, 23, 46, 61, 92, 122, 244, 1403, 2806, 5612

There is a total of 12 positive divisors.
The sum of these divisors is 10416.
The arithmetic mean is 868.

8 even divisors

2, 4, 46, 92, 122, 244, 2806, 5612

4 odd divisors

1, 23, 61, 1403

How to compute the divisors of 5612?

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 5612 by each of the numbers from 1 to 5612 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)

5612 / 1 = 5612 (the remainder is 0, so 1 is a divisor of 5612)
5612 / 2 = 2806 (the remainder is 0, so 2 is a divisor of 5612)
5612 / 3 = 1870.6666666667 (the remainder is 2, so 3 is not a divisor of 5612)
...
5612 / 5611 = 1.0001782213509 (the remainder is 1, so 5611 is not a divisor of 5612)
5612 / 5612 = 1 (the remainder is 0, so 5612 is a divisor of 5612)

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 5612 (i.e. 74.913283201312). 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 $\frac{N}{d} = D$ )

5612 / 1 = 5612 (the remainder is 0, so 1 and 5612 are divisors of 5612)
5612 / 2 = 2806 (the remainder is 0, so 2 and 2806 are divisors of 5612)
5612 / 3 = 1870.6666666667 (the remainder is 2, so 3 is not a divisor of 5612)
...
5612 / 73 = 76.876712328767 (the remainder is 64, so 73 is not a divisor of 5612)
5612 / 74 = 75.837837837838 (the remainder is 62, so 74 is not a divisor of 5612)