What are the divisors of 5671?

1, 53, 107, 5671

There is a total of 4 positive divisors.
The sum of these divisors is 5832.
The arithmetic mean is 1458.

4 odd divisors

1, 53, 107, 5671

How to compute the divisors of 5671?

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 5671 by each of the numbers from 1 to 5671 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)

5671 / 1 = 5671 (the remainder is 0, so 1 is a divisor of 5671)
5671 / 2 = 2835.5 (the remainder is 1, so 2 is not a divisor of 5671)
5671 / 3 = 1890.3333333333 (the remainder is 1, so 3 is not a divisor of 5671)
...
5671 / 5670 = 1.000176366843 (the remainder is 1, so 5670 is not a divisor of 5671)
5671 / 5671 = 1 (the remainder is 0, so 5671 is a divisor of 5671)

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 5671 (i.e. 75.306042254257). 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 $\frac{N}{d} = D$ )

5671 / 1 = 5671 (the remainder is 0, so 1 and 5671 are divisors of 5671)
5671 / 2 = 2835.5 (the remainder is 1, so 2 is not a divisor of 5671)
5671 / 3 = 1890.3333333333 (the remainder is 1, so 3 is not a divisor of 5671)
...
5671 / 74 = 76.635135135135 (the remainder is 47, so 74 is not a divisor of 5671)
5671 / 75 = 75.613333333333 (the remainder is 46, so 75 is not a divisor of 5671)