What are the divisors of 3629?

1, 19, 191, 3629

There is a total of 4 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 960.

4 odd divisors

1, 19, 191, 3629

How to compute the divisors of 3629?

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 3629 by each of the numbers from 1 to 3629 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)

3629 / 1 = 3629 (the remainder is 0, so 1 is a divisor of 3629)
3629 / 2 = 1814.5 (the remainder is 1, so 2 is not a divisor of 3629)
3629 / 3 = 1209.6666666667 (the remainder is 2, so 3 is not a divisor of 3629)
...
3629 / 3628 = 1.0002756339581 (the remainder is 1, so 3628 is not a divisor of 3629)
3629 / 3629 = 1 (the remainder is 0, so 3629 is a divisor of 3629)

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 3629 (i.e. 60.241181927316). 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 $\frac{N}{d} = D$ )

3629 / 1 = 3629 (the remainder is 0, so 1 and 3629 are divisors of 3629)
3629 / 2 = 1814.5 (the remainder is 1, so 2 is not a divisor of 3629)
3629 / 3 = 1209.6666666667 (the remainder is 2, so 3 is not a divisor of 3629)
...
3629 / 59 = 61.508474576271 (the remainder is 30, so 59 is not a divisor of 3629)
3629 / 60 = 60.483333333333 (the remainder is 29, so 60 is not a divisor of 3629)