What are the divisors of 7014?

1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507, 7014

There is a total of 16 positive divisors.
The sum of these divisors is 16128.
The arithmetic mean is 1008.

8 even divisors

2, 6, 14, 42, 334, 1002, 2338, 7014

8 odd divisors

1, 3, 7, 21, 167, 501, 1169, 3507

How to compute the divisors of 7014?

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 7014 by each of the numbers from 1 to 7014 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)

7014 / 1 = 7014 (the remainder is 0, so 1 is a divisor of 7014)
7014 / 2 = 3507 (the remainder is 0, so 2 is a divisor of 7014)
7014 / 3 = 2338 (the remainder is 0, so 3 is a divisor of 7014)
...
7014 / 7013 = 1.0001425923285 (the remainder is 1, so 7013 is not a divisor of 7014)
7014 / 7014 = 1 (the remainder is 0, so 7014 is a divisor of 7014)

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 7014 (i.e. 83.74962686484). 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 $\frac{N}{d} = D$ )

7014 / 1 = 7014 (the remainder is 0, so 1 and 7014 are divisors of 7014)
7014 / 2 = 3507 (the remainder is 0, so 2 and 3507 are divisors of 7014)
7014 / 3 = 2338 (the remainder is 0, so 3 and 2338 are divisors of 7014)
...
7014 / 82 = 85.536585365854 (the remainder is 44, so 82 is not a divisor of 7014)
7014 / 83 = 84.506024096386 (the remainder is 42, so 83 is not a divisor of 7014)