What are the divisors of 2144?

1, 2, 4, 8, 16, 32, 67, 134, 268, 536, 1072, 2144

There is a total of 12 positive divisors.
The sum of these divisors is 4284.
The arithmetic mean is 357.

10 even divisors

2, 4, 8, 16, 32, 134, 268, 536, 1072, 2144

2 odd divisors

1, 67

How to compute the divisors of 2144?

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 2144 by each of the numbers from 1 to 2144 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)

2144 / 1 = 2144 (the remainder is 0, so 1 is a divisor of 2144)
2144 / 2 = 1072 (the remainder is 0, so 2 is a divisor of 2144)
2144 / 3 = 714.66666666667 (the remainder is 2, so 3 is not a divisor of 2144)
...
2144 / 2143 = 1.0004666355576 (the remainder is 1, so 2143 is not a divisor of 2144)
2144 / 2144 = 1 (the remainder is 0, so 2144 is a divisor of 2144)

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 2144 (i.e. 46.303347611161). 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 $\frac{N}{d} = D$ )

2144 / 1 = 2144 (the remainder is 0, so 1 and 2144 are divisors of 2144)
2144 / 2 = 1072 (the remainder is 0, so 2 and 1072 are divisors of 2144)
2144 / 3 = 714.66666666667 (the remainder is 2, so 3 is not a divisor of 2144)
...
2144 / 45 = 47.644444444444 (the remainder is 29, so 45 is not a divisor of 2144)
2144 / 46 = 46.608695652174 (the remainder is 28, so 46 is not a divisor of 2144)