What are the divisors of 1579?

1, 1579

There is a total of 2 positive divisors.
The sum of these divisors is 1580.
The arithmetic mean is 790.

2 odd divisors

1, 1579

How to compute the divisors of 1579?

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 1579 by each of the numbers from 1 to 1579 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)

1579 / 1 = 1579 (the remainder is 0, so 1 is a divisor of 1579)
1579 / 2 = 789.5 (the remainder is 1, so 2 is not a divisor of 1579)
1579 / 3 = 526.33333333333 (the remainder is 1, so 3 is not a divisor of 1579)
...
1579 / 1578 = 1.0006337135615 (the remainder is 1, so 1578 is not a divisor of 1579)
1579 / 1579 = 1 (the remainder is 0, so 1579 is a divisor of 1579)

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 1579 (i.e. 39.736632972611). 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 $\frac{N}{d} = D$ )

1579 / 1 = 1579 (the remainder is 0, so 1 and 1579 are divisors of 1579)
1579 / 2 = 789.5 (the remainder is 1, so 2 is not a divisor of 1579)
1579 / 3 = 526.33333333333 (the remainder is 1, so 3 is not a divisor of 1579)
...
1579 / 38 = 41.552631578947 (the remainder is 21, so 38 is not a divisor of 1579)
1579 / 39 = 40.487179487179 (the remainder is 19, so 39 is not a divisor of 1579)