What are the divisors of 3014?

1, 2, 11, 22, 137, 274, 1507, 3014

There is a total of 8 positive divisors.
The sum of these divisors is 4968.
The arithmetic mean is 621.

4 even divisors

2, 22, 274, 3014

4 odd divisors

1, 11, 137, 1507

How to compute the divisors of 3014?

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 3014 by each of the numbers from 1 to 3014 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)

3014 / 1 = 3014 (the remainder is 0, so 1 is a divisor of 3014)
3014 / 2 = 1507 (the remainder is 0, so 2 is a divisor of 3014)
3014 / 3 = 1004.6666666667 (the remainder is 2, so 3 is not a divisor of 3014)
...
3014 / 3013 = 1.0003318951211 (the remainder is 1, so 3013 is not a divisor of 3014)
3014 / 3014 = 1 (the remainder is 0, so 3014 is a divisor of 3014)

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 3014 (i.e. 54.899908925243). 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 $\frac{N}{d} = D$ )

3014 / 1 = 3014 (the remainder is 0, so 1 and 3014 are divisors of 3014)
3014 / 2 = 1507 (the remainder is 0, so 2 and 1507 are divisors of 3014)
3014 / 3 = 1004.6666666667 (the remainder is 2, so 3 is not a divisor of 3014)
...
3014 / 53 = 56.867924528302 (the remainder is 46, so 53 is not a divisor of 3014)
3014 / 54 = 55.814814814815 (the remainder is 44, so 54 is not a divisor of 3014)