What are the divisors of 3254?

1, 2, 1627, 3254

There is a total of 4 positive divisors.
The sum of these divisors is 4884.
The arithmetic mean is 1221.

2 even divisors

2, 3254

2 odd divisors

1, 1627

How to compute the divisors of 3254?

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 3254 by each of the numbers from 1 to 3254 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)

3254 / 1 = 3254 (the remainder is 0, so 1 is a divisor of 3254)
3254 / 2 = 1627 (the remainder is 0, so 2 is a divisor of 3254)
3254 / 3 = 1084.6666666667 (the remainder is 2, so 3 is not a divisor of 3254)
...
3254 / 3253 = 1.000307408546 (the remainder is 1, so 3253 is not a divisor of 3254)
3254 / 3254 = 1 (the remainder is 0, so 3254 is a divisor of 3254)

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 3254 (i.e. 57.043842787807). 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 $\frac{N}{d} = D$ )

3254 / 1 = 3254 (the remainder is 0, so 1 and 3254 are divisors of 3254)
3254 / 2 = 1627 (the remainder is 0, so 2 and 1627 are divisors of 3254)
3254 / 3 = 1084.6666666667 (the remainder is 2, so 3 is not a divisor of 3254)
...
3254 / 56 = 58.107142857143 (the remainder is 6, so 56 is not a divisor of 3254)
3254 / 57 = 57.087719298246 (the remainder is 5, so 57 is not a divisor of 3254)