What are the divisors of 2784?

1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 32, 48, 58, 87, 96, 116, 174, 232, 348, 464, 696, 928, 1392, 2784

There is a total of 24 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 315.

20 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 58, 96, 116, 174, 232, 348, 464, 696, 928, 1392, 2784

4 odd divisors

1, 3, 29, 87

How to compute the divisors of 2784?

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 2784 by each of the numbers from 1 to 2784 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)

2784 / 1 = 2784 (the remainder is 0, so 1 is a divisor of 2784)
2784 / 2 = 1392 (the remainder is 0, so 2 is a divisor of 2784)
2784 / 3 = 928 (the remainder is 0, so 3 is a divisor of 2784)
...
2784 / 2783 = 1.00035932447 (the remainder is 1, so 2783 is not a divisor of 2784)
2784 / 2784 = 1 (the remainder is 0, so 2784 is a divisor of 2784)

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 2784 (i.e. 52.763623833092). 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 $\frac{N}{d} = D$ )

2784 / 1 = 2784 (the remainder is 0, so 1 and 2784 are divisors of 2784)
2784 / 2 = 1392 (the remainder is 0, so 2 and 1392 are divisors of 2784)
2784 / 3 = 928 (the remainder is 0, so 3 and 928 are divisors of 2784)
...
2784 / 51 = 54.588235294118 (the remainder is 30, so 51 is not a divisor of 2784)
2784 / 52 = 53.538461538462 (the remainder is 28, so 52 is not a divisor of 2784)