What are the divisors of 5672?

1, 2, 4, 8, 709, 1418, 2836, 5672

There is a total of 8 positive divisors.
The sum of these divisors is 10650.
The arithmetic mean is 1331.25.

6 even divisors

2, 4, 8, 1418, 2836, 5672

2 odd divisors

1, 709

How to compute the divisors of 5672?

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 5672 by each of the numbers from 1 to 5672 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)

5672 / 1 = 5672 (the remainder is 0, so 1 is a divisor of 5672)
5672 / 2 = 2836 (the remainder is 0, so 2 is a divisor of 5672)
5672 / 3 = 1890.6666666667 (the remainder is 2, so 3 is not a divisor of 5672)
...
5672 / 5671 = 1.0001763357433 (the remainder is 1, so 5671 is not a divisor of 5672)
5672 / 5672 = 1 (the remainder is 0, so 5672 is a divisor of 5672)

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 5672 (i.e. 75.312681535051). 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 $\frac{N}{d} = D$ )

5672 / 1 = 5672 (the remainder is 0, so 1 and 5672 are divisors of 5672)
5672 / 2 = 2836 (the remainder is 0, so 2 and 2836 are divisors of 5672)
5672 / 3 = 1890.6666666667 (the remainder is 2, so 3 is not a divisor of 5672)
...
5672 / 74 = 76.648648648649 (the remainder is 48, so 74 is not a divisor of 5672)
5672 / 75 = 75.626666666667 (the remainder is 47, so 75 is not a divisor of 5672)