What are the divisors of 634?

1, 2, 317, 634

There is a total of 4 positive divisors.
The sum of these divisors is 954.
The arithmetic mean is 238.5.

2 even divisors

2, 634

2 odd divisors

1, 317

How to compute the divisors of 634?

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 634 by each of the numbers from 1 to 634 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)

634 / 1 = 634 (the remainder is 0, so 1 is a divisor of 634)
634 / 2 = 317 (the remainder is 0, so 2 is a divisor of 634)
634 / 3 = 211.33333333333 (the remainder is 1, so 3 is not a divisor of 634)
...
634 / 633 = 1.001579778831 (the remainder is 1, so 633 is not a divisor of 634)
634 / 634 = 1 (the remainder is 0, so 634 is a divisor of 634)

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 634 (i.e. 25.179356624028). 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 $\frac{N}{d} = D$ )

634 / 1 = 634 (the remainder is 0, so 1 and 634 are divisors of 634)
634 / 2 = 317 (the remainder is 0, so 2 and 317 are divisors of 634)
634 / 3 = 211.33333333333 (the remainder is 1, so 3 is not a divisor of 634)
...
634 / 24 = 26.416666666667 (the remainder is 10, so 24 is not a divisor of 634)
634 / 25 = 25.36 (the remainder is 9, so 25 is not a divisor of 634)