What are the divisors of 4384?

1, 2, 4, 8, 16, 32, 137, 274, 548, 1096, 2192, 4384

There is a total of 12 positive divisors.
The sum of these divisors is 8694.
The arithmetic mean is 724.5.

10 even divisors

2, 4, 8, 16, 32, 274, 548, 1096, 2192, 4384

2 odd divisors

1, 137

How to compute the divisors of 4384?

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 4384 by each of the numbers from 1 to 4384 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)

4384 / 1 = 4384 (the remainder is 0, so 1 is a divisor of 4384)
4384 / 2 = 2192 (the remainder is 0, so 2 is a divisor of 4384)
4384 / 3 = 1461.3333333333 (the remainder is 1, so 3 is not a divisor of 4384)
...
4384 / 4383 = 1.0002281542323 (the remainder is 1, so 4383 is not a divisor of 4384)
4384 / 4384 = 1 (the remainder is 0, so 4384 is a divisor of 4384)

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 4384 (i.e. 66.211781428987). 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 $\frac{N}{d} = D$ )

4384 / 1 = 4384 (the remainder is 0, so 1 and 4384 are divisors of 4384)
4384 / 2 = 2192 (the remainder is 0, so 2 and 2192 are divisors of 4384)
4384 / 3 = 1461.3333333333 (the remainder is 1, so 3 is not a divisor of 4384)
...
4384 / 65 = 67.446153846154 (the remainder is 29, so 65 is not a divisor of 4384)
4384 / 66 = 66.424242424242 (the remainder is 28, so 66 is not a divisor of 4384)