What are the divisors of 3417?

1, 3, 17, 51, 67, 201, 1139, 3417

There is a total of 8 positive divisors.
The sum of these divisors is 4896.
The arithmetic mean is 612.

8 odd divisors

1, 3, 17, 51, 67, 201, 1139, 3417

How to compute the divisors of 3417?

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 3417 by each of the numbers from 1 to 3417 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)

3417 / 1 = 3417 (the remainder is 0, so 1 is a divisor of 3417)
3417 / 2 = 1708.5 (the remainder is 1, so 2 is not a divisor of 3417)
3417 / 3 = 1139 (the remainder is 0, so 3 is a divisor of 3417)
...
3417 / 3416 = 1.0002927400468 (the remainder is 1, so 3416 is not a divisor of 3417)
3417 / 3417 = 1 (the remainder is 0, so 3417 is a divisor of 3417)

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 3417 (i.e. 58.455110982702). 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 $\frac{N}{d} = D$ )

3417 / 1 = 3417 (the remainder is 0, so 1 and 3417 are divisors of 3417)
3417 / 2 = 1708.5 (the remainder is 1, so 2 is not a divisor of 3417)
3417 / 3 = 1139 (the remainder is 0, so 3 and 1139 are divisors of 3417)
...
3417 / 57 = 59.947368421053 (the remainder is 54, so 57 is not a divisor of 3417)
3417 / 58 = 58.913793103448 (the remainder is 53, so 58 is not a divisor of 3417)