What are the divisors of 3316?

1, 2, 4, 829, 1658, 3316

There is a total of 6 positive divisors.
The sum of these divisors is 5810.
The arithmetic mean is 968.33333333333.

4 even divisors

2, 4, 1658, 3316

2 odd divisors

1, 829

How to compute the divisors of 3316?

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 3316 by each of the numbers from 1 to 3316 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)

3316 / 1 = 3316 (the remainder is 0, so 1 is a divisor of 3316)
3316 / 2 = 1658 (the remainder is 0, so 2 is a divisor of 3316)
3316 / 3 = 1105.3333333333 (the remainder is 1, so 3 is not a divisor of 3316)
...
3316 / 3315 = 1.0003016591252 (the remainder is 1, so 3315 is not a divisor of 3316)
3316 / 3316 = 1 (the remainder is 0, so 3316 is a divisor of 3316)

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 3316 (i.e. 57.584720195552). 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 $\frac{N}{d} = D$ )

3316 / 1 = 3316 (the remainder is 0, so 1 and 3316 are divisors of 3316)
3316 / 2 = 1658 (the remainder is 0, so 2 and 1658 are divisors of 3316)
3316 / 3 = 1105.3333333333 (the remainder is 1, so 3 is not a divisor of 3316)
...
3316 / 56 = 59.214285714286 (the remainder is 12, so 56 is not a divisor of 3316)
3316 / 57 = 58.175438596491 (the remainder is 10, so 57 is not a divisor of 3316)