What are the divisors of 3698?

1, 2, 43, 86, 1849, 3698

There is a total of 6 positive divisors.
The sum of these divisors is 5679.
The arithmetic mean is 946.5.

3 even divisors

2, 86, 3698

3 odd divisors

1, 43, 1849

How to compute the divisors of 3698?

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 3698 by each of the numbers from 1 to 3698 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)

3698 / 1 = 3698 (the remainder is 0, so 1 is a divisor of 3698)
3698 / 2 = 1849 (the remainder is 0, so 2 is a divisor of 3698)
3698 / 3 = 1232.6666666667 (the remainder is 2, so 3 is not a divisor of 3698)
...
3698 / 3697 = 1.0002704895862 (the remainder is 1, so 3697 is not a divisor of 3698)
3698 / 3698 = 1 (the remainder is 0, so 3698 is a divisor of 3698)

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 3698 (i.e. 60.811183182043). 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 $\frac{N}{d} = D$ )

3698 / 1 = 3698 (the remainder is 0, so 1 and 3698 are divisors of 3698)
3698 / 2 = 1849 (the remainder is 0, so 2 and 1849 are divisors of 3698)
3698 / 3 = 1232.6666666667 (the remainder is 2, so 3 is not a divisor of 3698)
...
3698 / 59 = 62.677966101695 (the remainder is 40, so 59 is not a divisor of 3698)
3698 / 60 = 61.633333333333 (the remainder is 38, so 60 is not a divisor of 3698)