What are the divisors of 439?

1, 439

There is a total of 2 positive divisors.
The sum of these divisors is 440.
The arithmetic mean is 220.

2 odd divisors

1, 439

How to compute the divisors of 439?

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 439 by each of the numbers from 1 to 439 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)

439 / 1 = 439 (the remainder is 0, so 1 is a divisor of 439)
439 / 2 = 219.5 (the remainder is 1, so 2 is not a divisor of 439)
439 / 3 = 146.33333333333 (the remainder is 1, so 3 is not a divisor of 439)
...
439 / 438 = 1.0022831050228 (the remainder is 1, so 438 is not a divisor of 439)
439 / 439 = 1 (the remainder is 0, so 439 is a divisor of 439)

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 439 (i.e. 20.952326839757). 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 $\frac{N}{d} = D$ )

439 / 1 = 439 (the remainder is 0, so 1 and 439 are divisors of 439)
439 / 2 = 219.5 (the remainder is 1, so 2 is not a divisor of 439)
439 / 3 = 146.33333333333 (the remainder is 1, so 3 is not a divisor of 439)
...
439 / 19 = 23.105263157895 (the remainder is 2, so 19 is not a divisor of 439)
439 / 20 = 21.95 (the remainder is 19, so 20 is not a divisor of 439)