What are the divisors of 3347?

1, 3347

There is a total of 2 positive divisors.
The sum of these divisors is 3348.
The arithmetic mean is 1674.

2 odd divisors

1, 3347

How to compute the divisors of 3347?

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 3347 by each of the numbers from 1 to 3347 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)

3347 / 1 = 3347 (the remainder is 0, so 1 is a divisor of 3347)
3347 / 2 = 1673.5 (the remainder is 1, so 2 is not a divisor of 3347)
3347 / 3 = 1115.6666666667 (the remainder is 2, so 3 is not a divisor of 3347)
...
3347 / 3346 = 1.0002988643156 (the remainder is 1, so 3346 is not a divisor of 3347)
3347 / 3347 = 1 (the remainder is 0, so 3347 is a divisor of 3347)

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 3347 (i.e. 57.853262656483). 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 $\frac{N}{d} = D$ )

3347 / 1 = 3347 (the remainder is 0, so 1 and 3347 are divisors of 3347)
3347 / 2 = 1673.5 (the remainder is 1, so 2 is not a divisor of 3347)
3347 / 3 = 1115.6666666667 (the remainder is 2, so 3 is not a divisor of 3347)
...
3347 / 56 = 59.767857142857 (the remainder is 43, so 56 is not a divisor of 3347)
3347 / 57 = 58.719298245614 (the remainder is 41, so 57 is not a divisor of 3347)