What are the divisors of 376?

1, 2, 4, 8, 47, 94, 188, 376

There is a total of 8 positive divisors.
The sum of these divisors is 720.
The arithmetic mean is 90.

6 even divisors

2, 4, 8, 94, 188, 376

2 odd divisors

1, 47

How to compute the divisors of 376?

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 376 by each of the numbers from 1 to 376 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)

376 / 1 = 376 (the remainder is 0, so 1 is a divisor of 376)
376 / 2 = 188 (the remainder is 0, so 2 is a divisor of 376)
376 / 3 = 125.33333333333 (the remainder is 1, so 3 is not a divisor of 376)
...
376 / 375 = 1.0026666666667 (the remainder is 1, so 375 is not a divisor of 376)
376 / 376 = 1 (the remainder is 0, so 376 is a divisor of 376)

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 376 (i.e. 19.390719429665). 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 $\frac{N}{d} = D$ )

376 / 1 = 376 (the remainder is 0, so 1 and 376 are divisors of 376)
376 / 2 = 188 (the remainder is 0, so 2 and 188 are divisors of 376)
376 / 3 = 125.33333333333 (the remainder is 1, so 3 is not a divisor of 376)
...
376 / 18 = 20.888888888889 (the remainder is 16, so 18 is not a divisor of 376)
376 / 19 = 19.789473684211 (the remainder is 15, so 19 is not a divisor of 376)