What are the divisors of 2916?

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458, 2916

There is a total of 21 positive divisors.
The sum of these divisors is 7651.
The arithmetic mean is 364.33333333333.

14 even divisors

2, 4, 6, 12, 18, 36, 54, 108, 162, 324, 486, 972, 1458, 2916

7 odd divisors

1, 3, 9, 27, 81, 243, 729

How to compute the divisors of 2916?

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 2916 by each of the numbers from 1 to 2916 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)

2916 / 1 = 2916 (the remainder is 0, so 1 is a divisor of 2916)
2916 / 2 = 1458 (the remainder is 0, so 2 is a divisor of 2916)
2916 / 3 = 972 (the remainder is 0, so 3 is a divisor of 2916)
...
2916 / 2915 = 1.0003430531732 (the remainder is 1, so 2915 is not a divisor of 2916)
2916 / 2916 = 1 (the remainder is 0, so 2916 is a divisor of 2916)

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 2916 (i.e. 54). 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 $\frac{N}{d} = D$ )

2916 / 1 = 2916 (the remainder is 0, so 1 and 2916 are divisors of 2916)
2916 / 2 = 1458 (the remainder is 0, so 2 and 1458 are divisors of 2916)
2916 / 3 = 972 (the remainder is 0, so 3 and 972 are divisors of 2916)
...
2916 / 53 = 55.018867924528 (the remainder is 1, so 53 is not a divisor of 2916)
2916 / 54 = 54 (the remainder is 0, so 54 and 54 are divisors of 2916)