What are the divisors of 7019?

1, 7019

There is a total of 2 positive divisors.
The sum of these divisors is 7020.
The arithmetic mean is 3510.

2 odd divisors

1, 7019

How to compute the divisors of 7019?

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 7019 by each of the numbers from 1 to 7019 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)

7019 / 1 = 7019 (the remainder is 0, so 1 is a divisor of 7019)
7019 / 2 = 3509.5 (the remainder is 1, so 2 is not a divisor of 7019)
7019 / 3 = 2339.6666666667 (the remainder is 2, so 3 is not a divisor of 7019)
...
7019 / 7018 = 1.0001424907381 (the remainder is 1, so 7018 is not a divisor of 7019)
7019 / 7019 = 1 (the remainder is 0, so 7019 is a divisor of 7019)

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 7019 (i.e. 83.779472426126). 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 $\frac{N}{d} = D$ )

7019 / 1 = 7019 (the remainder is 0, so 1 and 7019 are divisors of 7019)
7019 / 2 = 3509.5 (the remainder is 1, so 2 is not a divisor of 7019)
7019 / 3 = 2339.6666666667 (the remainder is 2, so 3 is not a divisor of 7019)
...
7019 / 82 = 85.59756097561 (the remainder is 49, so 82 is not a divisor of 7019)
7019 / 83 = 84.566265060241 (the remainder is 47, so 83 is not a divisor of 7019)