What are the divisors of 337?

1, 337

There is a total of 2 positive divisors.
The sum of these divisors is 338.
The arithmetic mean is 169.

2 odd divisors

1, 337

How to compute the divisors of 337?

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 337 by each of the numbers from 1 to 337 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)

337 / 1 = 337 (the remainder is 0, so 1 is a divisor of 337)
337 / 2 = 168.5 (the remainder is 1, so 2 is not a divisor of 337)
337 / 3 = 112.33333333333 (the remainder is 1, so 3 is not a divisor of 337)
...
337 / 336 = 1.0029761904762 (the remainder is 1, so 336 is not a divisor of 337)
337 / 337 = 1 (the remainder is 0, so 337 is a divisor of 337)

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 337 (i.e. 18.357559750686). 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 $\frac{N}{d} = D$ )

337 / 1 = 337 (the remainder is 0, so 1 and 337 are divisors of 337)
337 / 2 = 168.5 (the remainder is 1, so 2 is not a divisor of 337)
337 / 3 = 112.33333333333 (the remainder is 1, so 3 is not a divisor of 337)
...
337 / 17 = 19.823529411765 (the remainder is 14, so 17 is not a divisor of 337)
337 / 18 = 18.722222222222 (the remainder is 13, so 18 is not a divisor of 337)