What are the divisors of 2379?

1, 3, 13, 39, 61, 183, 793, 2379

There is a total of 8 positive divisors.
The sum of these divisors is 3472.
The arithmetic mean is 434.

8 odd divisors

1, 3, 13, 39, 61, 183, 793, 2379

How to compute the divisors of 2379?

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 2379 by each of the numbers from 1 to 2379 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)

2379 / 1 = 2379 (the remainder is 0, so 1 is a divisor of 2379)
2379 / 2 = 1189.5 (the remainder is 1, so 2 is not a divisor of 2379)
2379 / 3 = 793 (the remainder is 0, so 3 is a divisor of 2379)
...
2379 / 2378 = 1.0004205214466 (the remainder is 1, so 2378 is not a divisor of 2379)
2379 / 2379 = 1 (the remainder is 0, so 2379 is a divisor of 2379)

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 2379 (i.e. 48.774993593029). 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 $\frac{N}{d} = D$ )

2379 / 1 = 2379 (the remainder is 0, so 1 and 2379 are divisors of 2379)
2379 / 2 = 1189.5 (the remainder is 1, so 2 is not a divisor of 2379)
2379 / 3 = 793 (the remainder is 0, so 3 and 793 are divisors of 2379)
...
2379 / 47 = 50.617021276596 (the remainder is 29, so 47 is not a divisor of 2379)
2379 / 48 = 49.5625 (the remainder is 27, so 48 is not a divisor of 2379)