What are the divisors of 3010?

1, 2, 5, 7, 10, 14, 35, 43, 70, 86, 215, 301, 430, 602, 1505, 3010

There is a total of 16 positive divisors.
The sum of these divisors is 6336.
The arithmetic mean is 396.

8 even divisors

2, 10, 14, 70, 86, 430, 602, 3010

8 odd divisors

1, 5, 7, 35, 43, 215, 301, 1505

How to compute the divisors of 3010?

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 3010 by each of the numbers from 1 to 3010 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)

3010 / 1 = 3010 (the remainder is 0, so 1 is a divisor of 3010)
3010 / 2 = 1505 (the remainder is 0, so 2 is a divisor of 3010)
3010 / 3 = 1003.3333333333 (the remainder is 1, so 3 is not a divisor of 3010)
...
3010 / 3009 = 1.0003323363244 (the remainder is 1, so 3009 is not a divisor of 3010)
3010 / 3010 = 1 (the remainder is 0, so 3010 is a divisor of 3010)

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 3010 (i.e. 54.863466897381). 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 $\frac{N}{d} = D$ )

3010 / 1 = 3010 (the remainder is 0, so 1 and 3010 are divisors of 3010)
3010 / 2 = 1505 (the remainder is 0, so 2 and 1505 are divisors of 3010)
3010 / 3 = 1003.3333333333 (the remainder is 1, so 3 is not a divisor of 3010)
...
3010 / 53 = 56.792452830189 (the remainder is 42, so 53 is not a divisor of 3010)
3010 / 54 = 55.740740740741 (the remainder is 40, so 54 is not a divisor of 3010)