What are the divisors of 1439?

1, 1439

There is a total of 2 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 720.

2 odd divisors

1, 1439

How to compute the divisors of 1439?

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 1439 by each of the numbers from 1 to 1439 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)

1439 / 1 = 1439 (the remainder is 0, so 1 is a divisor of 1439)
1439 / 2 = 719.5 (the remainder is 1, so 2 is not a divisor of 1439)
1439 / 3 = 479.66666666667 (the remainder is 2, so 3 is not a divisor of 1439)
...
1439 / 1438 = 1.0006954102921 (the remainder is 1, so 1438 is not a divisor of 1439)
1439 / 1439 = 1 (the remainder is 0, so 1439 is a divisor of 1439)

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 1439 (i.e. 37.934153476781). 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 $\frac{N}{d} = D$ )

1439 / 1 = 1439 (the remainder is 0, so 1 and 1439 are divisors of 1439)
1439 / 2 = 719.5 (the remainder is 1, so 2 is not a divisor of 1439)
1439 / 3 = 479.66666666667 (the remainder is 2, so 3 is not a divisor of 1439)
...
1439 / 36 = 39.972222222222 (the remainder is 35, so 36 is not a divisor of 1439)
1439 / 37 = 38.891891891892 (the remainder is 33, so 37 is not a divisor of 1439)