What are the divisors of 5350?

1, 2, 5, 10, 25, 50, 107, 214, 535, 1070, 2675, 5350

There is a total of 12 positive divisors.
The sum of these divisors is 10044.
The arithmetic mean is 837.

6 even divisors

2, 10, 50, 214, 1070, 5350

6 odd divisors

1, 5, 25, 107, 535, 2675

How to compute the divisors of 5350?

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 5350 by each of the numbers from 1 to 5350 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)

5350 / 1 = 5350 (the remainder is 0, so 1 is a divisor of 5350)
5350 / 2 = 2675 (the remainder is 0, so 2 is a divisor of 5350)
5350 / 3 = 1783.3333333333 (the remainder is 1, so 3 is not a divisor of 5350)
...
5350 / 5349 = 1.0001869508319 (the remainder is 1, so 5349 is not a divisor of 5350)
5350 / 5350 = 1 (the remainder is 0, so 5350 is a divisor of 5350)

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 5350 (i.e. 73.143694191639). 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 $\frac{N}{d} = D$ )

5350 / 1 = 5350 (the remainder is 0, so 1 and 5350 are divisors of 5350)
5350 / 2 = 2675 (the remainder is 0, so 2 and 2675 are divisors of 5350)
5350 / 3 = 1783.3333333333 (the remainder is 1, so 3 is not a divisor of 5350)
...
5350 / 72 = 74.305555555556 (the remainder is 22, so 72 is not a divisor of 5350)
5350 / 73 = 73.287671232877 (the remainder is 21, so 73 is not a divisor of 5350)