What are the divisors of 1598?

1, 2, 17, 34, 47, 94, 799, 1598

There is a total of 8 positive divisors.
The sum of these divisors is 2592.
The arithmetic mean is 324.

4 even divisors

2, 34, 94, 1598

4 odd divisors

1, 17, 47, 799

How to compute the divisors of 1598?

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 1598 by each of the numbers from 1 to 1598 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)

1598 / 1 = 1598 (the remainder is 0, so 1 is a divisor of 1598)
1598 / 2 = 799 (the remainder is 0, so 2 is a divisor of 1598)
1598 / 3 = 532.66666666667 (the remainder is 2, so 3 is not a divisor of 1598)
...
1598 / 1597 = 1.0006261740764 (the remainder is 1, so 1597 is not a divisor of 1598)
1598 / 1598 = 1 (the remainder is 0, so 1598 is a divisor of 1598)

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 1598 (i.e. 39.974992182613). 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 $\frac{N}{d} = D$ )

1598 / 1 = 1598 (the remainder is 0, so 1 and 1598 are divisors of 1598)
1598 / 2 = 799 (the remainder is 0, so 2 and 799 are divisors of 1598)
1598 / 3 = 532.66666666667 (the remainder is 2, so 3 is not a divisor of 1598)
...
1598 / 38 = 42.052631578947 (the remainder is 2, so 38 is not a divisor of 1598)
1598 / 39 = 40.974358974359 (the remainder is 38, so 39 is not a divisor of 1598)