What are the divisors of 5639?

1, 5639

There is a total of 2 positive divisors.
The sum of these divisors is 5640.
The arithmetic mean is 2820.

2 odd divisors

1, 5639

How to compute the divisors of 5639?

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 5639 by each of the numbers from 1 to 5639 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)

5639 / 1 = 5639 (the remainder is 0, so 1 is a divisor of 5639)
5639 / 2 = 2819.5 (the remainder is 1, so 2 is not a divisor of 5639)
5639 / 3 = 1879.6666666667 (the remainder is 2, so 3 is not a divisor of 5639)
...
5639 / 5638 = 1.0001773678609 (the remainder is 1, so 5638 is not a divisor of 5639)
5639 / 5639 = 1 (the remainder is 0, so 5639 is a divisor of 5639)

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 5639 (i.e. 75.093275331417). 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 $\frac{N}{d} = D$ )

5639 / 1 = 5639 (the remainder is 0, so 1 and 5639 are divisors of 5639)
5639 / 2 = 2819.5 (the remainder is 1, so 2 is not a divisor of 5639)
5639 / 3 = 1879.6666666667 (the remainder is 2, so 3 is not a divisor of 5639)
...
5639 / 74 = 76.202702702703 (the remainder is 15, so 74 is not a divisor of 5639)
5639 / 75 = 75.186666666667 (the remainder is 14, so 75 is not a divisor of 5639)