What are the divisors of 5206?

1, 2, 19, 38, 137, 274, 2603, 5206

There is a total of 8 positive divisors.
The sum of these divisors is 8280.
The arithmetic mean is 1035.

4 even divisors

2, 38, 274, 5206

4 odd divisors

1, 19, 137, 2603

How to compute the divisors of 5206?

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 5206 by each of the numbers from 1 to 5206 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)

5206 / 1 = 5206 (the remainder is 0, so 1 is a divisor of 5206)
5206 / 2 = 2603 (the remainder is 0, so 2 is a divisor of 5206)
5206 / 3 = 1735.3333333333 (the remainder is 1, so 3 is not a divisor of 5206)
...
5206 / 5205 = 1.0001921229587 (the remainder is 1, so 5205 is not a divisor of 5206)
5206 / 5206 = 1 (the remainder is 0, so 5206 is a divisor of 5206)

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 5206 (i.e. 72.15261603019). 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 $\frac{N}{d} = D$ )

5206 / 1 = 5206 (the remainder is 0, so 1 and 5206 are divisors of 5206)
5206 / 2 = 2603 (the remainder is 0, so 2 and 2603 are divisors of 5206)
5206 / 3 = 1735.3333333333 (the remainder is 1, so 3 is not a divisor of 5206)
...
5206 / 71 = 73.323943661972 (the remainder is 23, so 71 is not a divisor of 5206)
5206 / 72 = 72.305555555556 (the remainder is 22, so 72 is not a divisor of 5206)