What are the divisors of 6014?

1, 2, 31, 62, 97, 194, 3007, 6014

There is a total of 8 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 1176.

4 even divisors

2, 62, 194, 6014

4 odd divisors

1, 31, 97, 3007

How to compute the divisors of 6014?

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 6014 by each of the numbers from 1 to 6014 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)

6014 / 1 = 6014 (the remainder is 0, so 1 is a divisor of 6014)
6014 / 2 = 3007 (the remainder is 0, so 2 is a divisor of 6014)
6014 / 3 = 2004.6666666667 (the remainder is 2, so 3 is not a divisor of 6014)
...
6014 / 6013 = 1.0001663063363 (the remainder is 1, so 6013 is not a divisor of 6014)
6014 / 6014 = 1 (the remainder is 0, so 6014 is a divisor of 6014)

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 6014 (i.e. 77.549983881365). 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 $\frac{N}{d} = D$ )

6014 / 1 = 6014 (the remainder is 0, so 1 and 6014 are divisors of 6014)
6014 / 2 = 3007 (the remainder is 0, so 2 and 3007 are divisors of 6014)
6014 / 3 = 2004.6666666667 (the remainder is 2, so 3 is not a divisor of 6014)
...
6014 / 76 = 79.131578947368 (the remainder is 10, so 76 is not a divisor of 6014)
6014 / 77 = 78.103896103896 (the remainder is 8, so 77 is not a divisor of 6014)