What are the divisors of 5450?

1, 2, 5, 10, 25, 50, 109, 218, 545, 1090, 2725, 5450

There is a total of 12 positive divisors.
The sum of these divisors is 10230.
The arithmetic mean is 852.5.

6 even divisors

2, 10, 50, 218, 1090, 5450

6 odd divisors

1, 5, 25, 109, 545, 2725

How to compute the divisors of 5450?

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 5450 by each of the numbers from 1 to 5450 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)

5450 / 1 = 5450 (the remainder is 0, so 1 is a divisor of 5450)
5450 / 2 = 2725 (the remainder is 0, so 2 is a divisor of 5450)
5450 / 3 = 1816.6666666667 (the remainder is 2, so 3 is not a divisor of 5450)
...
5450 / 5449 = 1.0001835199119 (the remainder is 1, so 5449 is not a divisor of 5450)
5450 / 5450 = 1 (the remainder is 0, so 5450 is a divisor of 5450)

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 5450 (i.e. 73.824115301167). 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 $\frac{N}{d} = D$ )

5450 / 1 = 5450 (the remainder is 0, so 1 and 5450 are divisors of 5450)
5450 / 2 = 2725 (the remainder is 0, so 2 and 2725 are divisors of 5450)
5450 / 3 = 1816.6666666667 (the remainder is 2, so 3 is not a divisor of 5450)
...
5450 / 72 = 75.694444444444 (the remainder is 50, so 72 is not a divisor of 5450)
5450 / 73 = 74.657534246575 (the remainder is 48, so 73 is not a divisor of 5450)