What are the divisors of 5037?

1, 3, 23, 69, 73, 219, 1679, 5037

There is a total of 8 positive divisors.
The sum of these divisors is 7104.
The arithmetic mean is 888.

8 odd divisors

1, 3, 23, 69, 73, 219, 1679, 5037

How to compute the divisors of 5037?

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 5037 by each of the numbers from 1 to 5037 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)

5037 / 1 = 5037 (the remainder is 0, so 1 is a divisor of 5037)
5037 / 2 = 2518.5 (the remainder is 1, so 2 is not a divisor of 5037)
5037 / 3 = 1679 (the remainder is 0, so 3 is a divisor of 5037)
...
5037 / 5036 = 1.0001985702939 (the remainder is 1, so 5036 is not a divisor of 5037)
5037 / 5037 = 1 (the remainder is 0, so 5037 is a divisor of 5037)

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 5037 (i.e. 70.971825395716). 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 $\frac{N}{d} = D$ )

5037 / 1 = 5037 (the remainder is 0, so 1 and 5037 are divisors of 5037)
5037 / 2 = 2518.5 (the remainder is 1, so 2 is not a divisor of 5037)
5037 / 3 = 1679 (the remainder is 0, so 3 and 1679 are divisors of 5037)
...
5037 / 69 = 73 (the remainder is 0, so 69 and 73 are divisors of 5037)
5037 / 70 = 71.957142857143 (the remainder is 67, so 70 is not a divisor of 5037)