What are the divisors of 7016?

1, 2, 4, 8, 877, 1754, 3508, 7016

There is a total of 8 positive divisors.
The sum of these divisors is 13170.
The arithmetic mean is 1646.25.

6 even divisors

2, 4, 8, 1754, 3508, 7016

2 odd divisors

1, 877

How to compute the divisors of 7016?

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 7016 by each of the numbers from 1 to 7016 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)

7016 / 1 = 7016 (the remainder is 0, so 1 is a divisor of 7016)
7016 / 2 = 3508 (the remainder is 0, so 2 is a divisor of 7016)
7016 / 3 = 2338.6666666667 (the remainder is 2, so 3 is not a divisor of 7016)
...
7016 / 7015 = 1.000142551675 (the remainder is 1, so 7015 is not a divisor of 7016)
7016 / 7016 = 1 (the remainder is 0, so 7016 is a divisor of 7016)

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 7016 (i.e. 83.761566365488). 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 $\frac{N}{d} = D$ )

7016 / 1 = 7016 (the remainder is 0, so 1 and 7016 are divisors of 7016)
7016 / 2 = 3508 (the remainder is 0, so 2 and 3508 are divisors of 7016)
7016 / 3 = 2338.6666666667 (the remainder is 2, so 3 is not a divisor of 7016)
...
7016 / 82 = 85.560975609756 (the remainder is 46, so 82 is not a divisor of 7016)
7016 / 83 = 84.530120481928 (the remainder is 44, so 83 is not a divisor of 7016)