What are the divisors of 5029?

1, 47, 107, 5029

There is a total of 4 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 1296.

4 odd divisors

1, 47, 107, 5029

How to compute the divisors of 5029?

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 5029 by each of the numbers from 1 to 5029 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)

5029 / 1 = 5029 (the remainder is 0, so 1 is a divisor of 5029)
5029 / 2 = 2514.5 (the remainder is 1, so 2 is not a divisor of 5029)
5029 / 3 = 1676.3333333333 (the remainder is 1, so 3 is not a divisor of 5029)
...
5029 / 5028 = 1.0001988862371 (the remainder is 1, so 5028 is not a divisor of 5029)
5029 / 5029 = 1 (the remainder is 0, so 5029 is a divisor of 5029)

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 5029 (i.e. 70.915442605966). 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 $\frac{N}{d} = D$ )

5029 / 1 = 5029 (the remainder is 0, so 1 and 5029 are divisors of 5029)
5029 / 2 = 2514.5 (the remainder is 1, so 2 is not a divisor of 5029)
5029 / 3 = 1676.3333333333 (the remainder is 1, so 3 is not a divisor of 5029)
...
5029 / 69 = 72.884057971014 (the remainder is 61, so 69 is not a divisor of 5029)
5029 / 70 = 71.842857142857 (the remainder is 59, so 70 is not a divisor of 5029)