What are the divisors of 334?

1, 2, 167, 334

There is a total of 4 positive divisors.
The sum of these divisors is 504.
The arithmetic mean is 126.

2 even divisors

2, 334

2 odd divisors

1, 167

How to compute the divisors of 334?

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 334 by each of the numbers from 1 to 334 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)

334 / 1 = 334 (the remainder is 0, so 1 is a divisor of 334)
334 / 2 = 167 (the remainder is 0, so 2 is a divisor of 334)
334 / 3 = 111.33333333333 (the remainder is 1, so 3 is not a divisor of 334)
...
334 / 333 = 1.003003003003 (the remainder is 1, so 333 is not a divisor of 334)
334 / 334 = 1 (the remainder is 0, so 334 is a divisor of 334)

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 334 (i.e. 18.275666882497). 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 $\frac{N}{d} = D$ )

334 / 1 = 334 (the remainder is 0, so 1 and 334 are divisors of 334)
334 / 2 = 167 (the remainder is 0, so 2 and 167 are divisors of 334)
334 / 3 = 111.33333333333 (the remainder is 1, so 3 is not a divisor of 334)
...
334 / 17 = 19.647058823529 (the remainder is 11, so 17 is not a divisor of 334)
334 / 18 = 18.555555555556 (the remainder is 10, so 18 is not a divisor of 334)