What are the divisors of 3614?

1, 2, 13, 26, 139, 278, 1807, 3614

There is a total of 8 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 735.

4 even divisors

2, 26, 278, 3614

4 odd divisors

1, 13, 139, 1807

How to compute the divisors of 3614?

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 3614 by each of the numbers from 1 to 3614 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)

3614 / 1 = 3614 (the remainder is 0, so 1 is a divisor of 3614)
3614 / 2 = 1807 (the remainder is 0, so 2 is a divisor of 3614)
3614 / 3 = 1204.6666666667 (the remainder is 2, so 3 is not a divisor of 3614)
...
3614 / 3613 = 1.0002767783006 (the remainder is 1, so 3613 is not a divisor of 3614)
3614 / 3614 = 1 (the remainder is 0, so 3614 is a divisor of 3614)

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 3614 (i.e. 60.116553460757). 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 $\frac{N}{d} = D$ )

3614 / 1 = 3614 (the remainder is 0, so 1 and 3614 are divisors of 3614)
3614 / 2 = 1807 (the remainder is 0, so 2 and 1807 are divisors of 3614)
3614 / 3 = 1204.6666666667 (the remainder is 2, so 3 is not a divisor of 3614)
...
3614 / 59 = 61.254237288136 (the remainder is 15, so 59 is not a divisor of 3614)
3614 / 60 = 60.233333333333 (the remainder is 14, so 60 is not a divisor of 3614)