What are the divisors of 3610?

1, 2, 5, 10, 19, 38, 95, 190, 361, 722, 1805, 3610

There is a total of 12 positive divisors.
The sum of these divisors is 6858.
The arithmetic mean is 571.5.

6 even divisors

2, 10, 38, 190, 722, 3610

6 odd divisors

1, 5, 19, 95, 361, 1805

How to compute the divisors of 3610?

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 3610 by each of the numbers from 1 to 3610 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)

3610 / 1 = 3610 (the remainder is 0, so 1 is a divisor of 3610)
3610 / 2 = 1805 (the remainder is 0, so 2 is a divisor of 3610)
3610 / 3 = 1203.3333333333 (the remainder is 1, so 3 is not a divisor of 3610)
...
3610 / 3609 = 1.0002770850651 (the remainder is 1, so 3609 is not a divisor of 3610)
3610 / 3610 = 1 (the remainder is 0, so 3610 is a divisor of 3610)

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 3610 (i.e. 60.083275543199). 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 $\frac{N}{d} = D$ )

3610 / 1 = 3610 (the remainder is 0, so 1 and 3610 are divisors of 3610)
3610 / 2 = 1805 (the remainder is 0, so 2 and 1805 are divisors of 3610)
3610 / 3 = 1203.3333333333 (the remainder is 1, so 3 is not a divisor of 3610)
...
3610 / 59 = 61.186440677966 (the remainder is 11, so 59 is not a divisor of 3610)
3610 / 60 = 60.166666666667 (the remainder is 10, so 60 is not a divisor of 3610)