What are the divisors of 3626?

1, 2, 7, 14, 37, 49, 74, 98, 259, 518, 1813, 3626

There is a total of 12 positive divisors.
The sum of these divisors is 6498.
The arithmetic mean is 541.5.

6 even divisors

2, 14, 74, 98, 518, 3626

6 odd divisors

1, 7, 37, 49, 259, 1813

How to compute the divisors of 3626?

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 3626 by each of the numbers from 1 to 3626 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)

3626 / 1 = 3626 (the remainder is 0, so 1 is a divisor of 3626)
3626 / 2 = 1813 (the remainder is 0, so 2 is a divisor of 3626)
3626 / 3 = 1208.6666666667 (the remainder is 2, so 3 is not a divisor of 3626)
...
3626 / 3625 = 1.000275862069 (the remainder is 1, so 3625 is not a divisor of 3626)
3626 / 3626 = 1 (the remainder is 0, so 3626 is a divisor of 3626)

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 3626 (i.e. 60.216276869298). 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 $\frac{N}{d} = D$ )

3626 / 1 = 3626 (the remainder is 0, so 1 and 3626 are divisors of 3626)
3626 / 2 = 1813 (the remainder is 0, so 2 and 1813 are divisors of 3626)
3626 / 3 = 1208.6666666667 (the remainder is 2, so 3 is not a divisor of 3626)
...
3626 / 59 = 61.457627118644 (the remainder is 27, so 59 is not a divisor of 3626)
3626 / 60 = 60.433333333333 (the remainder is 26, so 60 is not a divisor of 3626)