What are the divisors of 2750?

1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 125, 250, 275, 550, 1375, 2750

There is a total of 16 positive divisors.
The sum of these divisors is 5616.
The arithmetic mean is 351.

8 even divisors

2, 10, 22, 50, 110, 250, 550, 2750

8 odd divisors

1, 5, 11, 25, 55, 125, 275, 1375

How to compute the divisors of 2750?

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 2750 by each of the numbers from 1 to 2750 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)

2750 / 1 = 2750 (the remainder is 0, so 1 is a divisor of 2750)
2750 / 2 = 1375 (the remainder is 0, so 2 is a divisor of 2750)
2750 / 3 = 916.66666666667 (the remainder is 2, so 3 is not a divisor of 2750)
...
2750 / 2749 = 1.0003637686431 (the remainder is 1, so 2749 is not a divisor of 2750)
2750 / 2750 = 1 (the remainder is 0, so 2750 is a divisor of 2750)

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 2750 (i.e. 52.440442408508). 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 $\frac{N}{d} = D$ )

2750 / 1 = 2750 (the remainder is 0, so 1 and 2750 are divisors of 2750)
2750 / 2 = 1375 (the remainder is 0, so 2 and 1375 are divisors of 2750)
2750 / 3 = 916.66666666667 (the remainder is 2, so 3 is not a divisor of 2750)
...
2750 / 51 = 53.921568627451 (the remainder is 47, so 51 is not a divisor of 2750)
2750 / 52 = 52.884615384615 (the remainder is 46, so 52 is not a divisor of 2750)