What are the divisors of 3272?

1, 2, 4, 8, 409, 818, 1636, 3272

There is a total of 8 positive divisors.
The sum of these divisors is 6150.
The arithmetic mean is 768.75.

6 even divisors

2, 4, 8, 818, 1636, 3272

2 odd divisors

1, 409

How to compute the divisors of 3272?

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 3272 by each of the numbers from 1 to 3272 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)

3272 / 1 = 3272 (the remainder is 0, so 1 is a divisor of 3272)
3272 / 2 = 1636 (the remainder is 0, so 2 is a divisor of 3272)
3272 / 3 = 1090.6666666667 (the remainder is 2, so 3 is not a divisor of 3272)
...
3272 / 3271 = 1.0003057169061 (the remainder is 1, so 3271 is not a divisor of 3272)
3272 / 3272 = 1 (the remainder is 0, so 3272 is a divisor of 3272)

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 3272 (i.e. 57.2013985843). 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 $\frac{N}{d} = D$ )

3272 / 1 = 3272 (the remainder is 0, so 1 and 3272 are divisors of 3272)
3272 / 2 = 1636 (the remainder is 0, so 2 and 1636 are divisors of 3272)
3272 / 3 = 1090.6666666667 (the remainder is 2, so 3 is not a divisor of 3272)
...
3272 / 56 = 58.428571428571 (the remainder is 24, so 56 is not a divisor of 3272)
3272 / 57 = 57.40350877193 (the remainder is 23, so 57 is not a divisor of 3272)