What are the divisors of 335?

1, 5, 67, 335

There is a total of 4 positive divisors.
The sum of these divisors is 408.
The arithmetic mean is 102.

4 odd divisors

1, 5, 67, 335

How to compute the divisors of 335?

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 335 by each of the numbers from 1 to 335 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)

335 / 1 = 335 (the remainder is 0, so 1 is a divisor of 335)
335 / 2 = 167.5 (the remainder is 1, so 2 is not a divisor of 335)
335 / 3 = 111.66666666667 (the remainder is 2, so 3 is not a divisor of 335)
...
335 / 334 = 1.002994011976 (the remainder is 1, so 334 is not a divisor of 335)
335 / 335 = 1 (the remainder is 0, so 335 is a divisor of 335)

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 335 (i.e. 18.303005217723). 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 $\frac{N}{d} = D$ )

335 / 1 = 335 (the remainder is 0, so 1 and 335 are divisors of 335)
335 / 2 = 167.5 (the remainder is 1, so 2 is not a divisor of 335)
335 / 3 = 111.66666666667 (the remainder is 2, so 3 is not a divisor of 335)
...
335 / 17 = 19.705882352941 (the remainder is 12, so 17 is not a divisor of 335)
335 / 18 = 18.611111111111 (the remainder is 11, so 18 is not a divisor of 335)