What are the divisors of 6020?

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 43, 70, 86, 140, 172, 215, 301, 430, 602, 860, 1204, 1505, 3010, 6020

There is a total of 24 positive divisors.
The sum of these divisors is 14784.
The arithmetic mean is 616.

16 even divisors

2, 4, 10, 14, 20, 28, 70, 86, 140, 172, 430, 602, 860, 1204, 3010, 6020

8 odd divisors

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

How to compute the divisors of 6020?

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 6020 by each of the numbers from 1 to 6020 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)

6020 / 1 = 6020 (the remainder is 0, so 1 is a divisor of 6020)
6020 / 2 = 3010 (the remainder is 0, so 2 is a divisor of 6020)
6020 / 3 = 2006.6666666667 (the remainder is 2, so 3 is not a divisor of 6020)
...
6020 / 6019 = 1.0001661405549 (the remainder is 1, so 6019 is not a divisor of 6020)
6020 / 6020 = 1 (the remainder is 0, so 6020 is a divisor of 6020)

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 6020 (i.e. 77.588658965083). 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 $\frac{N}{d} = D$ )

6020 / 1 = 6020 (the remainder is 0, so 1 and 6020 are divisors of 6020)
6020 / 2 = 3010 (the remainder is 0, so 2 and 3010 are divisors of 6020)
6020 / 3 = 2006.6666666667 (the remainder is 2, so 3 is not a divisor of 6020)
...
6020 / 76 = 79.210526315789 (the remainder is 16, so 76 is not a divisor of 6020)
6020 / 77 = 78.181818181818 (the remainder is 14, so 77 is not a divisor of 6020)