What are the divisors of 577?

1, 577

There is a total of 2 positive divisors.
The sum of these divisors is 578.
The arithmetic mean is 289.

2 odd divisors

1, 577

How to compute the divisors of 577?

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 577 by each of the numbers from 1 to 577 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)

577 / 1 = 577 (the remainder is 0, so 1 is a divisor of 577)
577 / 2 = 288.5 (the remainder is 1, so 2 is not a divisor of 577)
577 / 3 = 192.33333333333 (the remainder is 1, so 3 is not a divisor of 577)
...
577 / 576 = 1.0017361111111 (the remainder is 1, so 576 is not a divisor of 577)
577 / 577 = 1 (the remainder is 0, so 577 is a divisor of 577)

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 577 (i.e. 24.020824298929). 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 $\frac{N}{d} = D$ )

577 / 1 = 577 (the remainder is 0, so 1 and 577 are divisors of 577)
577 / 2 = 288.5 (the remainder is 1, so 2 is not a divisor of 577)
577 / 3 = 192.33333333333 (the remainder is 1, so 3 is not a divisor of 577)
...
577 / 23 = 25.086956521739 (the remainder is 2, so 23 is not a divisor of 577)
577 / 24 = 24.041666666667 (the remainder is 1, so 24 is not a divisor of 577)