What are the divisors of 3619?

1, 7, 11, 47, 77, 329, 517, 3619

There is a total of 8 positive divisors.
The sum of these divisors is 4608.
The arithmetic mean is 576.

8 odd divisors

1, 7, 11, 47, 77, 329, 517, 3619

How to compute the divisors of 3619?

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 3619 by each of the numbers from 1 to 3619 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)

3619 / 1 = 3619 (the remainder is 0, so 1 is a divisor of 3619)
3619 / 2 = 1809.5 (the remainder is 1, so 2 is not a divisor of 3619)
3619 / 3 = 1206.3333333333 (the remainder is 1, so 3 is not a divisor of 3619)
...
3619 / 3618 = 1.0002763957988 (the remainder is 1, so 3618 is not a divisor of 3619)
3619 / 3619 = 1 (the remainder is 0, so 3619 is a divisor of 3619)

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 3619 (i.e. 60.15812497078). 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 $\frac{N}{d} = D$ )

3619 / 1 = 3619 (the remainder is 0, so 1 and 3619 are divisors of 3619)
3619 / 2 = 1809.5 (the remainder is 1, so 2 is not a divisor of 3619)
3619 / 3 = 1206.3333333333 (the remainder is 1, so 3 is not a divisor of 3619)
...
3619 / 59 = 61.338983050847 (the remainder is 20, so 59 is not a divisor of 3619)
3619 / 60 = 60.316666666667 (the remainder is 19, so 60 is not a divisor of 3619)