What are the divisors of 6160?

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 28, 35, 40, 44, 55, 56, 70, 77, 80, 88, 110, 112, 140, 154, 176, 220, 280, 308, 385, 440, 560, 616, 770, 880, 1232, 1540, 3080, 6160

There is a total of 40 positive divisors.
The sum of these divisors is 17856.
The arithmetic mean is 446.4.

32 even divisors

2, 4, 8, 10, 14, 16, 20, 22, 28, 40, 44, 56, 70, 80, 88, 110, 112, 140, 154, 176, 220, 280, 308, 440, 560, 616, 770, 880, 1232, 1540, 3080, 6160

8 odd divisors

1, 5, 7, 11, 35, 55, 77, 385

How to compute the divisors of 6160?

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 6160 by each of the numbers from 1 to 6160 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)

6160 / 1 = 6160 (the remainder is 0, so 1 is a divisor of 6160)
6160 / 2 = 3080 (the remainder is 0, so 2 is a divisor of 6160)
6160 / 3 = 2053.3333333333 (the remainder is 1, so 3 is not a divisor of 6160)
...
6160 / 6159 = 1.0001623640201 (the remainder is 1, so 6159 is not a divisor of 6160)
6160 / 6160 = 1 (the remainder is 0, so 6160 is a divisor of 6160)

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 6160 (i.e. 78.485667481394). 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 $\frac{N}{d} = D$ )

6160 / 1 = 6160 (the remainder is 0, so 1 and 6160 are divisors of 6160)
6160 / 2 = 3080 (the remainder is 0, so 2 and 3080 are divisors of 6160)
6160 / 3 = 2053.3333333333 (the remainder is 1, so 3 is not a divisor of 6160)
...
6160 / 77 = 80 (the remainder is 0, so 77 and 80 are divisors of 6160)
6160 / 78 = 78.974358974359 (the remainder is 76, so 78 is not a divisor of 6160)