What are the divisors of 550?

1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550

There is a total of 12 positive divisors.
The sum of these divisors is 1116.
The arithmetic mean is 93.

6 even divisors

2, 10, 22, 50, 110, 550

6 odd divisors

1, 5, 11, 25, 55, 275

How to compute the divisors of 550?

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 550 by each of the numbers from 1 to 550 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)

550 / 1 = 550 (the remainder is 0, so 1 is a divisor of 550)
550 / 2 = 275 (the remainder is 0, so 2 is a divisor of 550)
550 / 3 = 183.33333333333 (the remainder is 1, so 3 is not a divisor of 550)
...
550 / 549 = 1.0018214936248 (the remainder is 1, so 549 is not a divisor of 550)
550 / 550 = 1 (the remainder is 0, so 550 is a divisor of 550)

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 550 (i.e. 23.452078799117). 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 $\frac{N}{d} = D$ )

550 / 1 = 550 (the remainder is 0, so 1 and 550 are divisors of 550)
550 / 2 = 275 (the remainder is 0, so 2 and 275 are divisors of 550)
550 / 3 = 183.33333333333 (the remainder is 1, so 3 is not a divisor of 550)
...
550 / 22 = 25 (the remainder is 0, so 22 and 25 are divisors of 550)
550 / 23 = 23.913043478261 (the remainder is 21, so 23 is not a divisor of 550)