What are the divisors of 626?

1, 2, 313, 626

There is a total of 4 positive divisors.
The sum of these divisors is 942.
The arithmetic mean is 235.5.

2 even divisors

2, 626

2 odd divisors

1, 313

How to compute the divisors of 626?

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 626 by each of the numbers from 1 to 626 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)

626 / 1 = 626 (the remainder is 0, so 1 is a divisor of 626)
626 / 2 = 313 (the remainder is 0, so 2 is a divisor of 626)
626 / 3 = 208.66666666667 (the remainder is 2, so 3 is not a divisor of 626)
...
626 / 625 = 1.0016 (the remainder is 1, so 625 is not a divisor of 626)
626 / 626 = 1 (the remainder is 0, so 626 is a divisor of 626)

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 626 (i.e. 25.019992006394). 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 $\frac{N}{d} = D$ )

626 / 1 = 626 (the remainder is 0, so 1 and 626 are divisors of 626)
626 / 2 = 313 (the remainder is 0, so 2 and 313 are divisors of 626)
626 / 3 = 208.66666666667 (the remainder is 2, so 3 is not a divisor of 626)
...
626 / 24 = 26.083333333333 (the remainder is 2, so 24 is not a divisor of 626)
626 / 25 = 25.04 (the remainder is 1, so 25 is not a divisor of 626)