What are the divisors of 5630?

1, 2, 5, 10, 563, 1126, 2815, 5630

There is a total of 8 positive divisors.
The sum of these divisors is 10152.
The arithmetic mean is 1269.

4 even divisors

2, 10, 1126, 5630

4 odd divisors

1, 5, 563, 2815

How to compute the divisors of 5630?

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 5630 by each of the numbers from 1 to 5630 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)

5630 / 1 = 5630 (the remainder is 0, so 1 is a divisor of 5630)
5630 / 2 = 2815 (the remainder is 0, so 2 is a divisor of 5630)
5630 / 3 = 1876.6666666667 (the remainder is 2, so 3 is not a divisor of 5630)
...
5630 / 5629 = 1.0001776514479 (the remainder is 1, so 5629 is not a divisor of 5630)
5630 / 5630 = 1 (the remainder is 0, so 5630 is a divisor of 5630)

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 5630 (i.e. 75.033325929216). 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 $\frac{N}{d} = D$ )

5630 / 1 = 5630 (the remainder is 0, so 1 and 5630 are divisors of 5630)
5630 / 2 = 2815 (the remainder is 0, so 2 and 2815 are divisors of 5630)
5630 / 3 = 1876.6666666667 (the remainder is 2, so 3 is not a divisor of 5630)
...
5630 / 74 = 76.081081081081 (the remainder is 6, so 74 is not a divisor of 5630)
5630 / 75 = 75.066666666667 (the remainder is 5, so 75 is not a divisor of 5630)