What are the divisors of 3694?

1, 2, 1847, 3694

There is a total of 4 positive divisors.
The sum of these divisors is 5544.
The arithmetic mean is 1386.

2 even divisors

2, 3694

2 odd divisors

1, 1847

How to compute the divisors of 3694?

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 3694 by each of the numbers from 1 to 3694 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)

3694 / 1 = 3694 (the remainder is 0, so 1 is a divisor of 3694)
3694 / 2 = 1847 (the remainder is 0, so 2 is a divisor of 3694)
3694 / 3 = 1231.3333333333 (the remainder is 1, so 3 is not a divisor of 3694)
...
3694 / 3693 = 1.0002707825616 (the remainder is 1, so 3693 is not a divisor of 3694)
3694 / 3694 = 1 (the remainder is 0, so 3694 is a divisor of 3694)

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 3694 (i.e. 60.778285596091). 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 $\frac{N}{d} = D$ )

3694 / 1 = 3694 (the remainder is 0, so 1 and 3694 are divisors of 3694)
3694 / 2 = 1847 (the remainder is 0, so 2 and 1847 are divisors of 3694)
3694 / 3 = 1231.3333333333 (the remainder is 1, so 3 is not a divisor of 3694)
...
3694 / 59 = 62.610169491525 (the remainder is 36, so 59 is not a divisor of 3694)
3694 / 60 = 61.566666666667 (the remainder is 34, so 60 is not a divisor of 3694)