What are the divisors of 5294?

1, 2, 2647, 5294

There is a total of 4 positive divisors.
The sum of these divisors is 7944.
The arithmetic mean is 1986.

2 even divisors

2, 5294

2 odd divisors

1, 2647

How to compute the divisors of 5294?

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 5294 by each of the numbers from 1 to 5294 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)

5294 / 1 = 5294 (the remainder is 0, so 1 is a divisor of 5294)
5294 / 2 = 2647 (the remainder is 0, so 2 is a divisor of 5294)
5294 / 3 = 1764.6666666667 (the remainder is 2, so 3 is not a divisor of 5294)
...
5294 / 5293 = 1.0001889287739 (the remainder is 1, so 5293 is not a divisor of 5294)
5294 / 5294 = 1 (the remainder is 0, so 5294 is a divisor of 5294)

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 5294 (i.e. 72.759879054325). 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 $\frac{N}{d} = D$ )

5294 / 1 = 5294 (the remainder is 0, so 1 and 5294 are divisors of 5294)
5294 / 2 = 2647 (the remainder is 0, so 2 and 2647 are divisors of 5294)
5294 / 3 = 1764.6666666667 (the remainder is 2, so 3 is not a divisor of 5294)
...
5294 / 71 = 74.56338028169 (the remainder is 40, so 71 is not a divisor of 5294)
5294 / 72 = 73.527777777778 (the remainder is 38, so 72 is not a divisor of 5294)