What are the divisors of 2922?

1, 2, 3, 6, 487, 974, 1461, 2922

There is a total of 8 positive divisors.
The sum of these divisors is 5856.
The arithmetic mean is 732.

4 even divisors

2, 6, 974, 2922

4 odd divisors

1, 3, 487, 1461

How to compute the divisors of 2922?

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 2922 by each of the numbers from 1 to 2922 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)

2922 / 1 = 2922 (the remainder is 0, so 1 is a divisor of 2922)
2922 / 2 = 1461 (the remainder is 0, so 2 is a divisor of 2922)
2922 / 3 = 974 (the remainder is 0, so 3 is a divisor of 2922)
...
2922 / 2921 = 1.0003423485108 (the remainder is 1, so 2921 is not a divisor of 2922)
2922 / 2922 = 1 (the remainder is 0, so 2922 is a divisor of 2922)

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 2922 (i.e. 54.055527006958). 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 $\frac{N}{d} = D$ )

2922 / 1 = 2922 (the remainder is 0, so 1 and 2922 are divisors of 2922)
2922 / 2 = 1461 (the remainder is 0, so 2 and 1461 are divisors of 2922)
2922 / 3 = 974 (the remainder is 0, so 3 and 974 are divisors of 2922)
...
2922 / 53 = 55.132075471698 (the remainder is 7, so 53 is not a divisor of 2922)
2922 / 54 = 54.111111111111 (the remainder is 6, so 54 is not a divisor of 2922)