What are the divisors of 7012?

1, 2, 4, 1753, 3506, 7012

There is a total of 6 positive divisors.
The sum of these divisors is 12278.
The arithmetic mean is 2046.3333333333.

4 even divisors

2, 4, 3506, 7012

2 odd divisors

1, 1753

How to compute the divisors of 7012?

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 7012 by each of the numbers from 1 to 7012 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)

7012 / 1 = 7012 (the remainder is 0, so 1 is a divisor of 7012)
7012 / 2 = 3506 (the remainder is 0, so 2 is a divisor of 7012)
7012 / 3 = 2337.3333333333 (the remainder is 1, so 3 is not a divisor of 7012)
...
7012 / 7011 = 1.0001426330053 (the remainder is 1, so 7011 is not a divisor of 7012)
7012 / 7012 = 1 (the remainder is 0, so 7012 is a divisor of 7012)

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 7012 (i.e. 83.737685661833). 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 $\frac{N}{d} = D$ )

7012 / 1 = 7012 (the remainder is 0, so 1 and 7012 are divisors of 7012)
7012 / 2 = 3506 (the remainder is 0, so 2 and 3506 are divisors of 7012)
7012 / 3 = 2337.3333333333 (the remainder is 1, so 3 is not a divisor of 7012)
...
7012 / 82 = 85.512195121951 (the remainder is 42, so 82 is not a divisor of 7012)
7012 / 83 = 84.481927710843 (the remainder is 40, so 83 is not a divisor of 7012)