What are the divisors of 7056?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 49, 56, 63, 72, 84, 98, 112, 126, 144, 147, 168, 196, 252, 294, 336, 392, 441, 504, 588, 784, 882, 1008, 1176, 1764, 2352, 3528, 7056

There is a total of 45 positive divisors.
The sum of these divisors is 22971.
The arithmetic mean is 510.46666666667.

36 even divisors

2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 36, 42, 48, 56, 72, 84, 98, 112, 126, 144, 168, 196, 252, 294, 336, 392, 504, 588, 784, 882, 1008, 1176, 1764, 2352, 3528, 7056

9 odd divisors

1, 3, 7, 9, 21, 49, 63, 147, 441

How to compute the divisors of 7056?

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 7056 by each of the numbers from 1 to 7056 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)

7056 / 1 = 7056 (the remainder is 0, so 1 is a divisor of 7056)
7056 / 2 = 3528 (the remainder is 0, so 2 is a divisor of 7056)
7056 / 3 = 2352 (the remainder is 0, so 3 is a divisor of 7056)
...
7056 / 7055 = 1.0001417434444 (the remainder is 1, so 7055 is not a divisor of 7056)
7056 / 7056 = 1 (the remainder is 0, so 7056 is a divisor of 7056)

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 7056 (i.e. 84). 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 $\frac{N}{d} = D$ )

7056 / 1 = 7056 (the remainder is 0, so 1 and 7056 are divisors of 7056)
7056 / 2 = 3528 (the remainder is 0, so 2 and 3528 are divisors of 7056)
7056 / 3 = 2352 (the remainder is 0, so 3 and 2352 are divisors of 7056)
...
7056 / 83 = 85.012048192771 (the remainder is 1, so 83 is not a divisor of 7056)
7056 / 84 = 84 (the remainder is 0, so 84 and 84 are divisors of 7056)