What are the divisors of 4424?

1, 2, 4, 7, 8, 14, 28, 56, 79, 158, 316, 553, 632, 1106, 2212, 4424

There is a total of 16 positive divisors.
The sum of these divisors is 9600.
The arithmetic mean is 600.

12 even divisors

2, 4, 8, 14, 28, 56, 158, 316, 632, 1106, 2212, 4424

4 odd divisors

1, 7, 79, 553

How to compute the divisors of 4424?

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 4424 by each of the numbers from 1 to 4424 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)

4424 / 1 = 4424 (the remainder is 0, so 1 is a divisor of 4424)
4424 / 2 = 2212 (the remainder is 0, so 2 is a divisor of 4424)
4424 / 3 = 1474.6666666667 (the remainder is 2, so 3 is not a divisor of 4424)
...
4424 / 4423 = 1.0002260908885 (the remainder is 1, so 4423 is not a divisor of 4424)
4424 / 4424 = 1 (the remainder is 0, so 4424 is a divisor of 4424)

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 4424 (i.e. 66.513156593264). 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 $\frac{N}{d} = D$ )

4424 / 1 = 4424 (the remainder is 0, so 1 and 4424 are divisors of 4424)
4424 / 2 = 2212 (the remainder is 0, so 2 and 2212 are divisors of 4424)
4424 / 3 = 1474.6666666667 (the remainder is 2, so 3 is not a divisor of 4424)
...
4424 / 65 = 68.061538461538 (the remainder is 4, so 65 is not a divisor of 4424)
4424 / 66 = 67.030303030303 (the remainder is 2, so 66 is not a divisor of 4424)