What are the divisors of 5274?

1, 2, 3, 6, 9, 18, 293, 586, 879, 1758, 2637, 5274

There is a total of 12 positive divisors.
The sum of these divisors is 11466.
The arithmetic mean is 955.5.

6 even divisors

2, 6, 18, 586, 1758, 5274

6 odd divisors

1, 3, 9, 293, 879, 2637

How to compute the divisors of 5274?

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 5274 by each of the numbers from 1 to 5274 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)

5274 / 1 = 5274 (the remainder is 0, so 1 is a divisor of 5274)
5274 / 2 = 2637 (the remainder is 0, so 2 is a divisor of 5274)
5274 / 3 = 1758 (the remainder is 0, so 3 is a divisor of 5274)
...
5274 / 5273 = 1.0001896453632 (the remainder is 1, so 5273 is not a divisor of 5274)
5274 / 5274 = 1 (the remainder is 0, so 5274 is a divisor of 5274)

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 5274 (i.e. 72.622310621461). 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 $\frac{N}{d} = D$ )

5274 / 1 = 5274 (the remainder is 0, so 1 and 5274 are divisors of 5274)
5274 / 2 = 2637 (the remainder is 0, so 2 and 2637 are divisors of 5274)
5274 / 3 = 1758 (the remainder is 0, so 3 and 1758 are divisors of 5274)
...
5274 / 71 = 74.281690140845 (the remainder is 20, so 71 is not a divisor of 5274)
5274 / 72 = 73.25 (the remainder is 18, so 72 is not a divisor of 5274)