What are the divisors of 5629?

1, 13, 433, 5629

There is a total of 4 positive divisors.
The sum of these divisors is 6076.
The arithmetic mean is 1519.

4 odd divisors

1, 13, 433, 5629

How to compute the divisors of 5629?

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 5629 by each of the numbers from 1 to 5629 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)

5629 / 1 = 5629 (the remainder is 0, so 1 is a divisor of 5629)
5629 / 2 = 2814.5 (the remainder is 1, so 2 is not a divisor of 5629)
5629 / 3 = 1876.3333333333 (the remainder is 1, so 3 is not a divisor of 5629)
...
5629 / 5628 = 1.0001776830135 (the remainder is 1, so 5628 is not a divisor of 5629)
5629 / 5629 = 1 (the remainder is 0, so 5629 is a divisor of 5629)

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 5629 (i.e. 75.026661927611). 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 $\frac{N}{d} = D$ )

5629 / 1 = 5629 (the remainder is 0, so 1 and 5629 are divisors of 5629)
5629 / 2 = 2814.5 (the remainder is 1, so 2 is not a divisor of 5629)
5629 / 3 = 1876.3333333333 (the remainder is 1, so 3 is not a divisor of 5629)
...
5629 / 74 = 76.067567567568 (the remainder is 5, so 74 is not a divisor of 5629)
5629 / 75 = 75.053333333333 (the remainder is 4, so 75 is not a divisor of 5629)