What are the divisors of 2892?

1, 2, 3, 4, 6, 12, 241, 482, 723, 964, 1446, 2892

There is a total of 12 positive divisors.
The sum of these divisors is 6776.
The arithmetic mean is 564.66666666667.

8 even divisors

2, 4, 6, 12, 482, 964, 1446, 2892

4 odd divisors

1, 3, 241, 723

How to compute the divisors of 2892?

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 2892 by each of the numbers from 1 to 2892 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)

2892 / 1 = 2892 (the remainder is 0, so 1 is a divisor of 2892)
2892 / 2 = 1446 (the remainder is 0, so 2 is a divisor of 2892)
2892 / 3 = 964 (the remainder is 0, so 3 is a divisor of 2892)
...
2892 / 2891 = 1.0003459010723 (the remainder is 1, so 2891 is not a divisor of 2892)
2892 / 2892 = 1 (the remainder is 0, so 2892 is a divisor of 2892)

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 2892 (i.e. 53.777318638995). 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 $\frac{N}{d} = D$ )

2892 / 1 = 2892 (the remainder is 0, so 1 and 2892 are divisors of 2892)
2892 / 2 = 1446 (the remainder is 0, so 2 and 1446 are divisors of 2892)
2892 / 3 = 964 (the remainder is 0, so 3 and 964 are divisors of 2892)
...
2892 / 52 = 55.615384615385 (the remainder is 32, so 52 is not a divisor of 2892)
2892 / 53 = 54.566037735849 (the remainder is 30, so 53 is not a divisor of 2892)