What are the divisors of 4432?

1, 2, 4, 8, 16, 277, 554, 1108, 2216, 4432

There is a total of 10 positive divisors.
The sum of these divisors is 8618.
The arithmetic mean is 861.8.

8 even divisors

2, 4, 8, 16, 554, 1108, 2216, 4432

2 odd divisors

1, 277

How to compute the divisors of 4432?

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 4432 by each of the numbers from 1 to 4432 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)

4432 / 1 = 4432 (the remainder is 0, so 1 is a divisor of 4432)
4432 / 2 = 2216 (the remainder is 0, so 2 is a divisor of 4432)
4432 / 3 = 1477.3333333333 (the remainder is 1, so 3 is not a divisor of 4432)
...
4432 / 4431 = 1.0002256826901 (the remainder is 1, so 4431 is not a divisor of 4432)
4432 / 4432 = 1 (the remainder is 0, so 4432 is a divisor of 4432)

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 4432 (i.e. 66.573267908373). 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 $\frac{N}{d} = D$ )

4432 / 1 = 4432 (the remainder is 0, so 1 and 4432 are divisors of 4432)
4432 / 2 = 2216 (the remainder is 0, so 2 and 2216 are divisors of 4432)
4432 / 3 = 1477.3333333333 (the remainder is 1, so 3 is not a divisor of 4432)
...
4432 / 65 = 68.184615384615 (the remainder is 12, so 65 is not a divisor of 4432)
4432 / 66 = 67.151515151515 (the remainder is 10, so 66 is not a divisor of 4432)