What are the divisors of 5266?

1, 2, 2633, 5266

There is a total of 4 positive divisors.
The sum of these divisors is 7902.
The arithmetic mean is 1975.5.

2 even divisors

2, 5266

2 odd divisors

1, 2633

How to compute the divisors of 5266?

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 5266 by each of the numbers from 1 to 5266 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)

5266 / 1 = 5266 (the remainder is 0, so 1 is a divisor of 5266)
5266 / 2 = 2633 (the remainder is 0, so 2 is a divisor of 5266)
5266 / 3 = 1755.3333333333 (the remainder is 1, so 3 is not a divisor of 5266)
...
5266 / 5265 = 1.0001899335233 (the remainder is 1, so 5265 is not a divisor of 5266)
5266 / 5266 = 1 (the remainder is 0, so 5266 is a divisor of 5266)

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 5266 (i.e. 72.567210226107). 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 $\frac{N}{d} = D$ )

5266 / 1 = 5266 (the remainder is 0, so 1 and 5266 are divisors of 5266)
5266 / 2 = 2633 (the remainder is 0, so 2 and 2633 are divisors of 5266)
5266 / 3 = 1755.3333333333 (the remainder is 1, so 3 is not a divisor of 5266)
...
5266 / 71 = 74.169014084507 (the remainder is 12, so 71 is not a divisor of 5266)
5266 / 72 = 73.138888888889 (the remainder is 10, so 72 is not a divisor of 5266)