What are the divisors of 838?

1, 2, 419, 838

There is a total of 4 positive divisors.
The sum of these divisors is 1260.
The arithmetic mean is 315.

2 even divisors

2, 838

2 odd divisors

1, 419

How to compute the divisors of 838?

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 838 by each of the numbers from 1 to 838 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)

838 / 1 = 838 (the remainder is 0, so 1 is a divisor of 838)
838 / 2 = 419 (the remainder is 0, so 2 is a divisor of 838)
838 / 3 = 279.33333333333 (the remainder is 1, so 3 is not a divisor of 838)
...
838 / 837 = 1.0011947431302 (the remainder is 1, so 837 is not a divisor of 838)
838 / 838 = 1 (the remainder is 0, so 838 is a divisor of 838)

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 838 (i.e. 28.94822965226). 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 $\frac{N}{d} = D$ )

838 / 1 = 838 (the remainder is 0, so 1 and 838 are divisors of 838)
838 / 2 = 419 (the remainder is 0, so 2 and 419 are divisors of 838)
838 / 3 = 279.33333333333 (the remainder is 1, so 3 is not a divisor of 838)
...
838 / 27 = 31.037037037037 (the remainder is 1, so 27 is not a divisor of 838)
838 / 28 = 29.928571428571 (the remainder is 26, so 28 is not a divisor of 838)