What are the divisors of 2744?

1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744

There is a total of 16 positive divisors.
The sum of these divisors is 6000.
The arithmetic mean is 375.

12 even divisors

2, 4, 8, 14, 28, 56, 98, 196, 392, 686, 1372, 2744

4 odd divisors

1, 7, 49, 343

How to compute the divisors of 2744?

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 2744 by each of the numbers from 1 to 2744 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)

2744 / 1 = 2744 (the remainder is 0, so 1 is a divisor of 2744)
2744 / 2 = 1372 (the remainder is 0, so 2 is a divisor of 2744)
2744 / 3 = 914.66666666667 (the remainder is 2, so 3 is not a divisor of 2744)
...
2744 / 2743 = 1.0003645643456 (the remainder is 1, so 2743 is not a divisor of 2744)
2744 / 2744 = 1 (the remainder is 0, so 2744 is a divisor of 2744)

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 2744 (i.e. 52.383203414835). 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 $\frac{N}{d} = D$ )

2744 / 1 = 2744 (the remainder is 0, so 1 and 2744 are divisors of 2744)
2744 / 2 = 1372 (the remainder is 0, so 2 and 1372 are divisors of 2744)
2744 / 3 = 914.66666666667 (the remainder is 2, so 3 is not a divisor of 2744)
...
2744 / 51 = 53.803921568627 (the remainder is 41, so 51 is not a divisor of 2744)
2744 / 52 = 52.769230769231 (the remainder is 40, so 52 is not a divisor of 2744)