What are the divisors of 5050?

1, 2, 5, 10, 25, 50, 101, 202, 505, 1010, 2525, 5050

There is a total of 12 positive divisors.
The sum of these divisors is 9486.
The arithmetic mean is 790.5.

6 even divisors

2, 10, 50, 202, 1010, 5050

6 odd divisors

1, 5, 25, 101, 505, 2525

How to compute the divisors of 5050?

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 5050 by each of the numbers from 1 to 5050 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)

5050 / 1 = 5050 (the remainder is 0, so 1 is a divisor of 5050)
5050 / 2 = 2525 (the remainder is 0, so 2 is a divisor of 5050)
5050 / 3 = 1683.3333333333 (the remainder is 1, so 3 is not a divisor of 5050)
...
5050 / 5049 = 1.0001980590216 (the remainder is 1, so 5049 is not a divisor of 5050)
5050 / 5050 = 1 (the remainder is 0, so 5050 is a divisor of 5050)

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 5050 (i.e. 71.063352017759). 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 $\frac{N}{d} = D$ )

5050 / 1 = 5050 (the remainder is 0, so 1 and 5050 are divisors of 5050)
5050 / 2 = 2525 (the remainder is 0, so 2 and 2525 are divisors of 5050)
5050 / 3 = 1683.3333333333 (the remainder is 1, so 3 is not a divisor of 5050)
...
5050 / 70 = 72.142857142857 (the remainder is 10, so 70 is not a divisor of 5050)
5050 / 71 = 71.12676056338 (the remainder is 9, so 71 is not a divisor of 5050)