What are the divisors of 3670?

1, 2, 5, 10, 367, 734, 1835, 3670

There is a total of 8 positive divisors.
The sum of these divisors is 6624.
The arithmetic mean is 828.

4 even divisors

2, 10, 734, 3670

4 odd divisors

1, 5, 367, 1835

How to compute the divisors of 3670?

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 3670 by each of the numbers from 1 to 3670 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)

3670 / 1 = 3670 (the remainder is 0, so 1 is a divisor of 3670)
3670 / 2 = 1835 (the remainder is 0, so 2 is a divisor of 3670)
3670 / 3 = 1223.3333333333 (the remainder is 1, so 3 is not a divisor of 3670)
...
3670 / 3669 = 1.0002725538294 (the remainder is 1, so 3669 is not a divisor of 3670)
3670 / 3670 = 1 (the remainder is 0, so 3670 is a divisor of 3670)

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 3670 (i.e. 60.580524923444). 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 $\frac{N}{d} = D$ )

3670 / 1 = 3670 (the remainder is 0, so 1 and 3670 are divisors of 3670)
3670 / 2 = 1835 (the remainder is 0, so 2 and 1835 are divisors of 3670)
3670 / 3 = 1223.3333333333 (the remainder is 1, so 3 is not a divisor of 3670)
...
3670 / 59 = 62.203389830508 (the remainder is 12, so 59 is not a divisor of 3670)
3670 / 60 = 61.166666666667 (the remainder is 10, so 60 is not a divisor of 3670)