What are the divisors of 3322?

1, 2, 11, 22, 151, 302, 1661, 3322

There is a total of 8 positive divisors.
The sum of these divisors is 5472.
The arithmetic mean is 684.

4 even divisors

2, 22, 302, 3322

4 odd divisors

1, 11, 151, 1661

How to compute the divisors of 3322?

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 3322 by each of the numbers from 1 to 3322 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)

3322 / 1 = 3322 (the remainder is 0, so 1 is a divisor of 3322)
3322 / 2 = 1661 (the remainder is 0, so 2 is a divisor of 3322)
3322 / 3 = 1107.3333333333 (the remainder is 1, so 3 is not a divisor of 3322)
...
3322 / 3321 = 1.0003011141223 (the remainder is 1, so 3321 is not a divisor of 3322)
3322 / 3322 = 1 (the remainder is 0, so 3322 is a divisor of 3322)

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 3322 (i.e. 57.636793803958). 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 $\frac{N}{d} = D$ )

3322 / 1 = 3322 (the remainder is 0, so 1 and 3322 are divisors of 3322)
3322 / 2 = 1661 (the remainder is 0, so 2 and 1661 are divisors of 3322)
3322 / 3 = 1107.3333333333 (the remainder is 1, so 3 is not a divisor of 3322)
...
3322 / 56 = 59.321428571429 (the remainder is 18, so 56 is not a divisor of 3322)
3322 / 57 = 58.280701754386 (the remainder is 16, so 57 is not a divisor of 3322)