What are the divisors of 2944?

1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 128, 184, 368, 736, 1472, 2944

There is a total of 16 positive divisors.
The sum of these divisors is 6120.
The arithmetic mean is 382.5.

14 even divisors

2, 4, 8, 16, 32, 46, 64, 92, 128, 184, 368, 736, 1472, 2944

2 odd divisors

1, 23

How to compute the divisors of 2944?

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 2944 by each of the numbers from 1 to 2944 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)

2944 / 1 = 2944 (the remainder is 0, so 1 is a divisor of 2944)
2944 / 2 = 1472 (the remainder is 0, so 2 is a divisor of 2944)
2944 / 3 = 981.33333333333 (the remainder is 1, so 3 is not a divisor of 2944)
...
2944 / 2943 = 1.0003397893306 (the remainder is 1, so 2943 is not a divisor of 2944)
2944 / 2944 = 1 (the remainder is 0, so 2944 is a divisor of 2944)

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 2944 (i.e. 54.258639865002). 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 $\frac{N}{d} = D$ )

2944 / 1 = 2944 (the remainder is 0, so 1 and 2944 are divisors of 2944)
2944 / 2 = 1472 (the remainder is 0, so 2 and 1472 are divisors of 2944)
2944 / 3 = 981.33333333333 (the remainder is 1, so 3 is not a divisor of 2944)
...
2944 / 53 = 55.547169811321 (the remainder is 29, so 53 is not a divisor of 2944)
2944 / 54 = 54.518518518519 (the remainder is 28, so 54 is not a divisor of 2944)