What are the divisors of 5030?

1, 2, 5, 10, 503, 1006, 2515, 5030

There is a total of 8 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 1134.

4 even divisors

2, 10, 1006, 5030

4 odd divisors

1, 5, 503, 2515

How to compute the divisors of 5030?

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 5030 by each of the numbers from 1 to 5030 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)

5030 / 1 = 5030 (the remainder is 0, so 1 is a divisor of 5030)
5030 / 2 = 2515 (the remainder is 0, so 2 is a divisor of 5030)
5030 / 3 = 1676.6666666667 (the remainder is 2, so 3 is not a divisor of 5030)
...
5030 / 5029 = 1.0001988466892 (the remainder is 1, so 5029 is not a divisor of 5030)
5030 / 5030 = 1 (the remainder is 0, so 5030 is a divisor of 5030)

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 5030 (i.e. 70.922492905989). 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 $\frac{N}{d} = D$ )

5030 / 1 = 5030 (the remainder is 0, so 1 and 5030 are divisors of 5030)
5030 / 2 = 2515 (the remainder is 0, so 2 and 2515 are divisors of 5030)
5030 / 3 = 1676.6666666667 (the remainder is 2, so 3 is not a divisor of 5030)
...
5030 / 69 = 72.898550724638 (the remainder is 62, so 69 is not a divisor of 5030)
5030 / 70 = 71.857142857143 (the remainder is 60, so 70 is not a divisor of 5030)