What are the divisors of 617?

1, 617

There is a total of 2 positive divisors.
The sum of these divisors is 618.
The arithmetic mean is 309.

2 odd divisors

1, 617

How to compute the divisors of 617?

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 617 by each of the numbers from 1 to 617 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)

617 / 1 = 617 (the remainder is 0, so 1 is a divisor of 617)
617 / 2 = 308.5 (the remainder is 1, so 2 is not a divisor of 617)
617 / 3 = 205.66666666667 (the remainder is 2, so 3 is not a divisor of 617)
...
617 / 616 = 1.0016233766234 (the remainder is 1, so 616 is not a divisor of 617)
617 / 617 = 1 (the remainder is 0, so 617 is a divisor of 617)

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 617 (i.e. 24.839484696748). 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 $\frac{N}{d} = D$ )

617 / 1 = 617 (the remainder is 0, so 1 and 617 are divisors of 617)
617 / 2 = 308.5 (the remainder is 1, so 2 is not a divisor of 617)
617 / 3 = 205.66666666667 (the remainder is 2, so 3 is not a divisor of 617)
...
617 / 23 = 26.826086956522 (the remainder is 19, so 23 is not a divisor of 617)
617 / 24 = 25.708333333333 (the remainder is 17, so 24 is not a divisor of 617)