What are the divisors of 336?

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336

There is a total of 20 positive divisors.
The sum of these divisors is 992.
The arithmetic mean is 49.6.

16 even divisors

2, 4, 6, 8, 12, 14, 16, 24, 28, 42, 48, 56, 84, 112, 168, 336

4 odd divisors

1, 3, 7, 21

How to compute the divisors of 336?

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 336 by each of the numbers from 1 to 336 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)

336 / 1 = 336 (the remainder is 0, so 1 is a divisor of 336)
336 / 2 = 168 (the remainder is 0, so 2 is a divisor of 336)
336 / 3 = 112 (the remainder is 0, so 3 is a divisor of 336)
...
336 / 335 = 1.0029850746269 (the remainder is 1, so 335 is not a divisor of 336)
336 / 336 = 1 (the remainder is 0, so 336 is a divisor of 336)

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 336 (i.e. 18.330302779823). 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 $\frac{N}{d} = D$ )

336 / 1 = 336 (the remainder is 0, so 1 and 336 are divisors of 336)
336 / 2 = 168 (the remainder is 0, so 2 and 168 are divisors of 336)
336 / 3 = 112 (the remainder is 0, so 3 and 112 are divisors of 336)
...
336 / 17 = 19.764705882353 (the remainder is 13, so 17 is not a divisor of 336)
336 / 18 = 18.666666666667 (the remainder is 12, so 18 is not a divisor of 336)