What are the divisors of 5194?

1, 2, 7, 14, 49, 53, 98, 106, 371, 742, 2597, 5194

There is a total of 12 positive divisors.
The sum of these divisors is 9234.
The arithmetic mean is 769.5.

6 even divisors

2, 14, 98, 106, 742, 5194

6 odd divisors

1, 7, 49, 53, 371, 2597

How to compute the divisors of 5194?

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 5194 by each of the numbers from 1 to 5194 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)

5194 / 1 = 5194 (the remainder is 0, so 1 is a divisor of 5194)
5194 / 2 = 2597 (the remainder is 0, so 2 is a divisor of 5194)
5194 / 3 = 1731.3333333333 (the remainder is 1, so 3 is not a divisor of 5194)
...
5194 / 5193 = 1.000192566917 (the remainder is 1, so 5193 is not a divisor of 5194)
5194 / 5194 = 1 (the remainder is 0, so 5194 is a divisor of 5194)

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 5194 (i.e. 72.069410986909). 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 $\frac{N}{d} = D$ )

5194 / 1 = 5194 (the remainder is 0, so 1 and 5194 are divisors of 5194)
5194 / 2 = 2597 (the remainder is 0, so 2 and 2597 are divisors of 5194)
5194 / 3 = 1731.3333333333 (the remainder is 1, so 3 is not a divisor of 5194)
...
5194 / 71 = 73.154929577465 (the remainder is 11, so 71 is not a divisor of 5194)
5194 / 72 = 72.138888888889 (the remainder is 10, so 72 is not a divisor of 5194)