What are the divisors of 5572?

1, 2, 4, 7, 14, 28, 199, 398, 796, 1393, 2786, 5572

There is a total of 12 positive divisors.
The sum of these divisors is 11200.
The arithmetic mean is 933.33333333333.

8 even divisors

2, 4, 14, 28, 398, 796, 2786, 5572

4 odd divisors

1, 7, 199, 1393

How to compute the divisors of 5572?

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 5572 by each of the numbers from 1 to 5572 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)

5572 / 1 = 5572 (the remainder is 0, so 1 is a divisor of 5572)
5572 / 2 = 2786 (the remainder is 0, so 2 is a divisor of 5572)
5572 / 3 = 1857.3333333333 (the remainder is 1, so 3 is not a divisor of 5572)
...
5572 / 5571 = 1.0001795009873 (the remainder is 1, so 5571 is not a divisor of 5572)
5572 / 5572 = 1 (the remainder is 0, so 5572 is a divisor of 5572)

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 5572 (i.e. 74.645830426086). 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 $\frac{N}{d} = D$ )

5572 / 1 = 5572 (the remainder is 0, so 1 and 5572 are divisors of 5572)
5572 / 2 = 2786 (the remainder is 0, so 2 and 2786 are divisors of 5572)
5572 / 3 = 1857.3333333333 (the remainder is 1, so 3 is not a divisor of 5572)
...
5572 / 73 = 76.328767123288 (the remainder is 24, so 73 is not a divisor of 5572)
5572 / 74 = 75.297297297297 (the remainder is 22, so 74 is not a divisor of 5572)