What are the divisors of 2800?

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800

There is a total of 30 positive divisors.
The sum of these divisors is 7688.
The arithmetic mean is 256.26666666667.

24 even divisors

2, 4, 8, 10, 14, 16, 20, 28, 40, 50, 56, 70, 80, 100, 112, 140, 200, 280, 350, 400, 560, 700, 1400, 2800

6 odd divisors

1, 5, 7, 25, 35, 175

How to compute the divisors of 2800?

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 2800 by each of the numbers from 1 to 2800 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)

2800 / 1 = 2800 (the remainder is 0, so 1 is a divisor of 2800)
2800 / 2 = 1400 (the remainder is 0, so 2 is a divisor of 2800)
2800 / 3 = 933.33333333333 (the remainder is 1, so 3 is not a divisor of 2800)
...
2800 / 2799 = 1.0003572704537 (the remainder is 1, so 2799 is not a divisor of 2800)
2800 / 2800 = 1 (the remainder is 0, so 2800 is a divisor of 2800)

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 2800 (i.e. 52.915026221292). 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 $\frac{N}{d} = D$ )

2800 / 1 = 2800 (the remainder is 0, so 1 and 2800 are divisors of 2800)
2800 / 2 = 1400 (the remainder is 0, so 2 and 1400 are divisors of 2800)
2800 / 3 = 933.33333333333 (the remainder is 1, so 3 is not a divisor of 2800)
...
2800 / 51 = 54.901960784314 (the remainder is 46, so 51 is not a divisor of 2800)
2800 / 52 = 53.846153846154 (the remainder is 44, so 52 is not a divisor of 2800)