What are the divisors of 2919?

1, 3, 7, 21, 139, 417, 973, 2919

There is a total of 8 positive divisors.
The sum of these divisors is 4480.
The arithmetic mean is 560.

8 odd divisors

1, 3, 7, 21, 139, 417, 973, 2919

How to compute the divisors of 2919?

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 2919 by each of the numbers from 1 to 2919 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)

2919 / 1 = 2919 (the remainder is 0, so 1 is a divisor of 2919)
2919 / 2 = 1459.5 (the remainder is 1, so 2 is not a divisor of 2919)
2919 / 3 = 973 (the remainder is 0, so 3 is a divisor of 2919)
...
2919 / 2918 = 1.0003427004798 (the remainder is 1, so 2918 is not a divisor of 2919)
2919 / 2919 = 1 (the remainder is 0, so 2919 is a divisor of 2919)

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 2919 (i.e. 54.02777063696). 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 $\frac{N}{d} = D$ )

2919 / 1 = 2919 (the remainder is 0, so 1 and 2919 are divisors of 2919)
2919 / 2 = 1459.5 (the remainder is 1, so 2 is not a divisor of 2919)
2919 / 3 = 973 (the remainder is 0, so 3 and 973 are divisors of 2919)
...
2919 / 53 = 55.075471698113 (the remainder is 4, so 53 is not a divisor of 2919)
2919 / 54 = 54.055555555556 (the remainder is 3, so 54 is not a divisor of 2919)