What are the divisors of 629?

1, 17, 37, 629

There is a total of 4 positive divisors.
The sum of these divisors is 684.
The arithmetic mean is 171.

4 odd divisors

1, 17, 37, 629

How to compute the divisors of 629?

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 629 by each of the numbers from 1 to 629 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)

629 / 1 = 629 (the remainder is 0, so 1 is a divisor of 629)
629 / 2 = 314.5 (the remainder is 1, so 2 is not a divisor of 629)
629 / 3 = 209.66666666667 (the remainder is 2, so 3 is not a divisor of 629)
...
629 / 628 = 1.0015923566879 (the remainder is 1, so 628 is not a divisor of 629)
629 / 629 = 1 (the remainder is 0, so 629 is a divisor of 629)

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 629 (i.e. 25.079872407969). 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 $\frac{N}{d} = D$ )

629 / 1 = 629 (the remainder is 0, so 1 and 629 are divisors of 629)
629 / 2 = 314.5 (the remainder is 1, so 2 is not a divisor of 629)
629 / 3 = 209.66666666667 (the remainder is 2, so 3 is not a divisor of 629)
...
629 / 24 = 26.208333333333 (the remainder is 5, so 24 is not a divisor of 629)
629 / 25 = 25.16 (the remainder is 4, so 25 is not a divisor of 629)