What are the divisors of 2772?

1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 28, 33, 36, 42, 44, 63, 66, 77, 84, 99, 126, 132, 154, 198, 231, 252, 308, 396, 462, 693, 924, 1386, 2772

There is a total of 36 positive divisors.
The sum of these divisors is 8736.
The arithmetic mean is 242.66666666667.

24 even divisors

2, 4, 6, 12, 14, 18, 22, 28, 36, 42, 44, 66, 84, 126, 132, 154, 198, 252, 308, 396, 462, 924, 1386, 2772

12 odd divisors

1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693

How to compute the divisors of 2772?

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 2772 by each of the numbers from 1 to 2772 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)

2772 / 1 = 2772 (the remainder is 0, so 1 is a divisor of 2772)
2772 / 2 = 1386 (the remainder is 0, so 2 is a divisor of 2772)
2772 / 3 = 924 (the remainder is 0, so 3 is a divisor of 2772)
...
2772 / 2771 = 1.0003608805485 (the remainder is 1, so 2771 is not a divisor of 2772)
2772 / 2772 = 1 (the remainder is 0, so 2772 is a divisor of 2772)

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 2772 (i.e. 52.649786324353). 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 $\frac{N}{d} = D$ )

2772 / 1 = 2772 (the remainder is 0, so 1 and 2772 are divisors of 2772)
2772 / 2 = 1386 (the remainder is 0, so 2 and 1386 are divisors of 2772)
2772 / 3 = 924 (the remainder is 0, so 3 and 924 are divisors of 2772)
...
2772 / 51 = 54.352941176471 (the remainder is 18, so 51 is not a divisor of 2772)
2772 / 52 = 53.307692307692 (the remainder is 16, so 52 is not a divisor of 2772)