What are the divisors of 619?

1, 619

There is a total of 2 positive divisors.
The sum of these divisors is 620.
The arithmetic mean is 310.

2 odd divisors

1, 619

How to compute the divisors of 619?

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 619 by each of the numbers from 1 to 619 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)

619 / 1 = 619 (the remainder is 0, so 1 is a divisor of 619)
619 / 2 = 309.5 (the remainder is 1, so 2 is not a divisor of 619)
619 / 3 = 206.33333333333 (the remainder is 1, so 3 is not a divisor of 619)
...
619 / 618 = 1.0016181229773 (the remainder is 1, so 618 is not a divisor of 619)
619 / 619 = 1 (the remainder is 0, so 619 is a divisor of 619)

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 619 (i.e. 24.879710609249). 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 $\frac{N}{d} = D$ )

619 / 1 = 619 (the remainder is 0, so 1 and 619 are divisors of 619)
619 / 2 = 309.5 (the remainder is 1, so 2 is not a divisor of 619)
619 / 3 = 206.33333333333 (the remainder is 1, so 3 is not a divisor of 619)
...
619 / 23 = 26.913043478261 (the remainder is 21, so 23 is not a divisor of 619)
619 / 24 = 25.791666666667 (the remainder is 19, so 24 is not a divisor of 619)