What are the divisors of 3598?

1, 2, 7, 14, 257, 514, 1799, 3598

There is a total of 8 positive divisors.
The sum of these divisors is 6192.
The arithmetic mean is 774.

4 even divisors

2, 14, 514, 3598

4 odd divisors

1, 7, 257, 1799

How to compute the divisors of 3598?

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 3598 by each of the numbers from 1 to 3598 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)

3598 / 1 = 3598 (the remainder is 0, so 1 is a divisor of 3598)
3598 / 2 = 1799 (the remainder is 0, so 2 is a divisor of 3598)
3598 / 3 = 1199.3333333333 (the remainder is 1, so 3 is not a divisor of 3598)
...
3598 / 3597 = 1.0002780094523 (the remainder is 1, so 3597 is not a divisor of 3598)
3598 / 3598 = 1 (the remainder is 0, so 3598 is a divisor of 3598)

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 3598 (i.e. 59.983331017875). 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 $\frac{N}{d} = D$ )

3598 / 1 = 3598 (the remainder is 0, so 1 and 3598 are divisors of 3598)
3598 / 2 = 1799 (the remainder is 0, so 2 and 1799 are divisors of 3598)
3598 / 3 = 1199.3333333333 (the remainder is 1, so 3 is not a divisor of 3598)
...
3598 / 58 = 62.034482758621 (the remainder is 2, so 58 is not a divisor of 3598)
3598 / 59 = 60.983050847458 (the remainder is 58, so 59 is not a divisor of 3598)