What are the divisors of 7008?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008

There is a total of 24 positive divisors.
The sum of these divisors is 18648.
The arithmetic mean is 777.

20 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 96, 146, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008

4 odd divisors

1, 3, 73, 219

How to compute the divisors of 7008?

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 7008 by each of the numbers from 1 to 7008 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)

7008 / 1 = 7008 (the remainder is 0, so 1 is a divisor of 7008)
7008 / 2 = 3504 (the remainder is 0, so 2 is a divisor of 7008)
7008 / 3 = 2336 (the remainder is 0, so 3 is a divisor of 7008)
...
7008 / 7007 = 1.0001427144284 (the remainder is 1, so 7007 is not a divisor of 7008)
7008 / 7008 = 1 (the remainder is 0, so 7008 is a divisor of 7008)

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 7008 (i.e. 83.713798145825). 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 $\frac{N}{d} = D$ )

7008 / 1 = 7008 (the remainder is 0, so 1 and 7008 are divisors of 7008)
7008 / 2 = 3504 (the remainder is 0, so 2 and 3504 are divisors of 7008)
7008 / 3 = 2336 (the remainder is 0, so 3 and 2336 are divisors of 7008)
...
7008 / 82 = 85.463414634146 (the remainder is 38, so 82 is not a divisor of 7008)
7008 / 83 = 84.433734939759 (the remainder is 36, so 83 is not a divisor of 7008)