What are the divisors of 2550?

1, 2, 3, 5, 6, 10, 15, 17, 25, 30, 34, 50, 51, 75, 85, 102, 150, 170, 255, 425, 510, 850, 1275, 2550

There is a total of 24 positive divisors.
The sum of these divisors is 6696.
The arithmetic mean is 279.

12 even divisors

2, 6, 10, 30, 34, 50, 102, 150, 170, 510, 850, 2550

12 odd divisors

1, 3, 5, 15, 17, 25, 51, 75, 85, 255, 425, 1275

How to compute the divisors of 2550?

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 2550 by each of the numbers from 1 to 2550 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)

2550 / 1 = 2550 (the remainder is 0, so 1 is a divisor of 2550)
2550 / 2 = 1275 (the remainder is 0, so 2 is a divisor of 2550)
2550 / 3 = 850 (the remainder is 0, so 3 is a divisor of 2550)
...
2550 / 2549 = 1.0003923107101 (the remainder is 1, so 2549 is not a divisor of 2550)
2550 / 2550 = 1 (the remainder is 0, so 2550 is a divisor of 2550)

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 2550 (i.e. 50.49752469181). 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 $\frac{N}{d} = D$ )

2550 / 1 = 2550 (the remainder is 0, so 1 and 2550 are divisors of 2550)
2550 / 2 = 1275 (the remainder is 0, so 2 and 1275 are divisors of 2550)
2550 / 3 = 850 (the remainder is 0, so 3 and 850 are divisors of 2550)
...
2550 / 49 = 52.040816326531 (the remainder is 2, so 49 is not a divisor of 2550)
2550 / 50 = 51 (the remainder is 0, so 50 and 51 are divisors of 2550)