What are the divisors of 4436?

1, 2, 4, 1109, 2218, 4436

There is a total of 6 positive divisors.
The sum of these divisors is 7770.
The arithmetic mean is 1295.

4 even divisors

2, 4, 2218, 4436

2 odd divisors

1, 1109

How to compute the divisors of 4436?

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 4436 by each of the numbers from 1 to 4436 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)

4436 / 1 = 4436 (the remainder is 0, so 1 is a divisor of 4436)
4436 / 2 = 2218 (the remainder is 0, so 2 is a divisor of 4436)
4436 / 3 = 1478.6666666667 (the remainder is 2, so 3 is not a divisor of 4436)
...
4436 / 4435 = 1.0002254791432 (the remainder is 1, so 4435 is not a divisor of 4436)
4436 / 4436 = 1 (the remainder is 0, so 4436 is a divisor of 4436)

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 4436 (i.e. 66.603303221387). 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 $\frac{N}{d} = D$ )

4436 / 1 = 4436 (the remainder is 0, so 1 and 4436 are divisors of 4436)
4436 / 2 = 2218 (the remainder is 0, so 2 and 2218 are divisors of 4436)
4436 / 3 = 1478.6666666667 (the remainder is 2, so 3 is not a divisor of 4436)
...
4436 / 65 = 68.246153846154 (the remainder is 16, so 65 is not a divisor of 4436)
4436 / 66 = 67.212121212121 (the remainder is 14, so 66 is not a divisor of 4436)