What are the divisors of 7058?

1, 2, 3529, 7058

There is a total of 4 positive divisors.
The sum of these divisors is 10590.
The arithmetic mean is 2647.5.

2 even divisors

2, 7058

2 odd divisors

1, 3529

How to compute the divisors of 7058?

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 7058 by each of the numbers from 1 to 7058 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)

7058 / 1 = 7058 (the remainder is 0, so 1 is a divisor of 7058)
7058 / 2 = 3529 (the remainder is 0, so 2 is a divisor of 7058)
7058 / 3 = 2352.6666666667 (the remainder is 2, so 3 is not a divisor of 7058)
...
7058 / 7057 = 1.0001417032733 (the remainder is 1, so 7057 is not a divisor of 7058)
7058 / 7058 = 1 (the remainder is 0, so 7058 is a divisor of 7058)

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 7058 (i.e. 84.011903918433). 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 $\frac{N}{d} = D$ )

7058 / 1 = 7058 (the remainder is 0, so 1 and 7058 are divisors of 7058)
7058 / 2 = 3529 (the remainder is 0, so 2 and 3529 are divisors of 7058)
7058 / 3 = 2352.6666666667 (the remainder is 2, so 3 is not a divisor of 7058)
...
7058 / 83 = 85.036144578313 (the remainder is 3, so 83 is not a divisor of 7058)
7058 / 84 = 84.02380952381 (the remainder is 2, so 84 is not a divisor of 7058)