What are the divisors of 647?

1, 647

There is a total of 2 positive divisors.
The sum of these divisors is 648.
The arithmetic mean is 324.

2 odd divisors

1, 647

How to compute the divisors of 647?

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 647 by each of the numbers from 1 to 647 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)

647 / 1 = 647 (the remainder is 0, so 1 is a divisor of 647)
647 / 2 = 323.5 (the remainder is 1, so 2 is not a divisor of 647)
647 / 3 = 215.66666666667 (the remainder is 2, so 3 is not a divisor of 647)
...
647 / 646 = 1.0015479876161 (the remainder is 1, so 646 is not a divisor of 647)
647 / 647 = 1 (the remainder is 0, so 647 is a divisor of 647)

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 647 (i.e. 25.436194683954). 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 $\frac{N}{d} = D$ )

647 / 1 = 647 (the remainder is 0, so 1 and 647 are divisors of 647)
647 / 2 = 323.5 (the remainder is 1, so 2 is not a divisor of 647)
647 / 3 = 215.66666666667 (the remainder is 2, so 3 is not a divisor of 647)
...
647 / 24 = 26.958333333333 (the remainder is 23, so 24 is not a divisor of 647)
647 / 25 = 25.88 (the remainder is 22, so 25 is not a divisor of 647)