What are the divisors of 2378?

1, 2, 29, 41, 58, 82, 1189, 2378

There is a total of 8 positive divisors.
The sum of these divisors is 3780.
The arithmetic mean is 472.5.

4 even divisors

2, 58, 82, 2378

4 odd divisors

1, 29, 41, 1189

How to compute the divisors of 2378?

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 2378 by each of the numbers from 1 to 2378 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)

2378 / 1 = 2378 (the remainder is 0, so 1 is a divisor of 2378)
2378 / 2 = 1189 (the remainder is 0, so 2 is a divisor of 2378)
2378 / 3 = 792.66666666667 (the remainder is 2, so 3 is not a divisor of 2378)
...
2378 / 2377 = 1.0004206983593 (the remainder is 1, so 2377 is not a divisor of 2378)
2378 / 2378 = 1 (the remainder is 0, so 2378 is a divisor of 2378)

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 2378 (i.e. 48.764741360946). 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 $\frac{N}{d} = D$ )

2378 / 1 = 2378 (the remainder is 0, so 1 and 2378 are divisors of 2378)
2378 / 2 = 1189 (the remainder is 0, so 2 and 1189 are divisors of 2378)
2378 / 3 = 792.66666666667 (the remainder is 2, so 3 is not a divisor of 2378)
...
2378 / 47 = 50.595744680851 (the remainder is 28, so 47 is not a divisor of 2378)
2378 / 48 = 49.541666666667 (the remainder is 26, so 48 is not a divisor of 2378)