What are the divisors of 3314?

1, 2, 1657, 3314

There is a total of 4 positive divisors.
The sum of these divisors is 4974.
The arithmetic mean is 1243.5.

2 even divisors

2, 3314

2 odd divisors

1, 1657

How to compute the divisors of 3314?

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 3314 by each of the numbers from 1 to 3314 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)

3314 / 1 = 3314 (the remainder is 0, so 1 is a divisor of 3314)
3314 / 2 = 1657 (the remainder is 0, so 2 is a divisor of 3314)
3314 / 3 = 1104.6666666667 (the remainder is 2, so 3 is not a divisor of 3314)
...
3314 / 3313 = 1.0003018412315 (the remainder is 1, so 3313 is not a divisor of 3314)
3314 / 3314 = 1 (the remainder is 0, so 3314 is a divisor of 3314)

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 3314 (i.e. 57.567351858497). 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 $\frac{N}{d} = D$ )

3314 / 1 = 3314 (the remainder is 0, so 1 and 3314 are divisors of 3314)
3314 / 2 = 1657 (the remainder is 0, so 2 and 1657 are divisors of 3314)
3314 / 3 = 1104.6666666667 (the remainder is 2, so 3 is not a divisor of 3314)
...
3314 / 56 = 59.178571428571 (the remainder is 10, so 56 is not a divisor of 3314)
3314 / 57 = 58.140350877193 (the remainder is 8, so 57 is not a divisor of 3314)