What are the divisors of 380?

1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

There is a total of 12 positive divisors.
The sum of these divisors is 840.
The arithmetic mean is 70.

8 even divisors

2, 4, 10, 20, 38, 76, 190, 380

4 odd divisors

1, 5, 19, 95

How to compute the divisors of 380?

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 380 by each of the numbers from 1 to 380 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)

380 / 1 = 380 (the remainder is 0, so 1 is a divisor of 380)
380 / 2 = 190 (the remainder is 0, so 2 is a divisor of 380)
380 / 3 = 126.66666666667 (the remainder is 2, so 3 is not a divisor of 380)
...
380 / 379 = 1.0026385224274 (the remainder is 1, so 379 is not a divisor of 380)
380 / 380 = 1 (the remainder is 0, so 380 is a divisor of 380)

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 380 (i.e. 19.493588689618). 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 $\frac{N}{d} = D$ )

380 / 1 = 380 (the remainder is 0, so 1 and 380 are divisors of 380)
380 / 2 = 190 (the remainder is 0, so 2 and 190 are divisors of 380)
380 / 3 = 126.66666666667 (the remainder is 2, so 3 is not a divisor of 380)
...
380 / 18 = 21.111111111111 (the remainder is 2, so 18 is not a divisor of 380)
380 / 19 = 20 (the remainder is 0, so 19 and 20 are divisors of 380)