What are the divisors of 3579?

1, 3, 1193, 3579

There is a total of 4 positive divisors.
The sum of these divisors is 4776.
The arithmetic mean is 1194.

4 odd divisors

1, 3, 1193, 3579

How to compute the divisors of 3579?

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 3579 by each of the numbers from 1 to 3579 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)

3579 / 1 = 3579 (the remainder is 0, so 1 is a divisor of 3579)
3579 / 2 = 1789.5 (the remainder is 1, so 2 is not a divisor of 3579)
3579 / 3 = 1193 (the remainder is 0, so 3 is a divisor of 3579)
...
3579 / 3578 = 1.0002794857462 (the remainder is 1, so 3578 is not a divisor of 3579)
3579 / 3579 = 1 (the remainder is 0, so 3579 is a divisor of 3579)

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 3579 (i.e. 59.824744044584). 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 $\frac{N}{d} = D$ )

3579 / 1 = 3579 (the remainder is 0, so 1 and 3579 are divisors of 3579)
3579 / 2 = 1789.5 (the remainder is 1, so 2 is not a divisor of 3579)
3579 / 3 = 1193 (the remainder is 0, so 3 and 1193 are divisors of 3579)
...
3579 / 58 = 61.706896551724 (the remainder is 41, so 58 is not a divisor of 3579)
3579 / 59 = 60.661016949153 (the remainder is 39, so 59 is not a divisor of 3579)