What are the divisors of 6136?

1, 2, 4, 8, 13, 26, 52, 59, 104, 118, 236, 472, 767, 1534, 3068, 6136

There is a total of 16 positive divisors.
The sum of these divisors is 12600.
The arithmetic mean is 787.5.

12 even divisors

2, 4, 8, 26, 52, 104, 118, 236, 472, 1534, 3068, 6136

4 odd divisors

1, 13, 59, 767

How to compute the divisors of 6136?

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 6136 by each of the numbers from 1 to 6136 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)

6136 / 1 = 6136 (the remainder is 0, so 1 is a divisor of 6136)
6136 / 2 = 3068 (the remainder is 0, so 2 is a divisor of 6136)
6136 / 3 = 2045.3333333333 (the remainder is 1, so 3 is not a divisor of 6136)
...
6136 / 6135 = 1.000162999185 (the remainder is 1, so 6135 is not a divisor of 6136)
6136 / 6136 = 1 (the remainder is 0, so 6136 is a divisor of 6136)

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 6136 (i.e. 78.332624110265). 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 $\frac{N}{d} = D$ )

6136 / 1 = 6136 (the remainder is 0, so 1 and 6136 are divisors of 6136)
6136 / 2 = 3068 (the remainder is 0, so 2 and 3068 are divisors of 6136)
6136 / 3 = 2045.3333333333 (the remainder is 1, so 3 is not a divisor of 6136)
...
6136 / 77 = 79.688311688312 (the remainder is 53, so 77 is not a divisor of 6136)
6136 / 78 = 78.666666666667 (the remainder is 52, so 78 is not a divisor of 6136)