What are the divisors of 1056?

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056

There is a total of 24 positive divisors.
The sum of these divisors is 3024.
The arithmetic mean is 126.

20 even divisors

2, 4, 6, 8, 12, 16, 22, 24, 32, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056

4 odd divisors

1, 3, 11, 33

How to compute the divisors of 1056?

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 1056 by each of the numbers from 1 to 1056 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)

1056 / 1 = 1056 (the remainder is 0, so 1 is a divisor of 1056)
1056 / 2 = 528 (the remainder is 0, so 2 is a divisor of 1056)
1056 / 3 = 352 (the remainder is 0, so 3 is a divisor of 1056)
...
1056 / 1055 = 1.0009478672986 (the remainder is 1, so 1055 is not a divisor of 1056)
1056 / 1056 = 1 (the remainder is 0, so 1056 is a divisor of 1056)

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 1056 (i.e. 32.496153618544). 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 $\frac{N}{d} = D$ )

1056 / 1 = 1056 (the remainder is 0, so 1 and 1056 are divisors of 1056)
1056 / 2 = 528 (the remainder is 0, so 2 and 528 are divisors of 1056)
1056 / 3 = 352 (the remainder is 0, so 3 and 352 are divisors of 1056)
...
1056 / 31 = 34.064516129032 (the remainder is 2, so 31 is not a divisor of 1056)
1056 / 32 = 33 (the remainder is 0, so 32 and 33 are divisors of 1056)