What are the divisors of 3019?

1, 3019

There is a total of 2 positive divisors.
The sum of these divisors is 3020.
The arithmetic mean is 1510.

2 odd divisors

1, 3019

How to compute the divisors of 3019?

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 3019 by each of the numbers from 1 to 3019 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)

3019 / 1 = 3019 (the remainder is 0, so 1 is a divisor of 3019)
3019 / 2 = 1509.5 (the remainder is 1, so 2 is not a divisor of 3019)
3019 / 3 = 1006.3333333333 (the remainder is 1, so 3 is not a divisor of 3019)
...
3019 / 3018 = 1.0003313452618 (the remainder is 1, so 3018 is not a divisor of 3019)
3019 / 3019 = 1 (the remainder is 0, so 3019 is a divisor of 3019)

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 3019 (i.e. 54.945427471265). 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 $\frac{N}{d} = D$ )

3019 / 1 = 3019 (the remainder is 0, so 1 and 3019 are divisors of 3019)
3019 / 2 = 1509.5 (the remainder is 1, so 2 is not a divisor of 3019)
3019 / 3 = 1006.3333333333 (the remainder is 1, so 3 is not a divisor of 3019)
...
3019 / 53 = 56.962264150943 (the remainder is 51, so 53 is not a divisor of 3019)
3019 / 54 = 55.907407407407 (the remainder is 49, so 54 is not a divisor of 3019)