What are the divisors of 6113?

1, 6113

There is a total of 2 positive divisors.
The sum of these divisors is 6114.
The arithmetic mean is 3057.

2 odd divisors

1, 6113

How to compute the divisors of 6113?

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 6113 by each of the numbers from 1 to 6113 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)

6113 / 1 = 6113 (the remainder is 0, so 1 is a divisor of 6113)
6113 / 2 = 3056.5 (the remainder is 1, so 2 is not a divisor of 6113)
6113 / 3 = 2037.6666666667 (the remainder is 2, so 3 is not a divisor of 6113)
...
6113 / 6112 = 1.0001636125654 (the remainder is 1, so 6112 is not a divisor of 6113)
6113 / 6113 = 1 (the remainder is 0, so 6113 is a divisor of 6113)

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 6113 (i.e. 78.185676437568). 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 $\frac{N}{d} = D$ )

6113 / 1 = 6113 (the remainder is 0, so 1 and 6113 are divisors of 6113)
6113 / 2 = 3056.5 (the remainder is 1, so 2 is not a divisor of 6113)
6113 / 3 = 2037.6666666667 (the remainder is 2, so 3 is not a divisor of 6113)
...
6113 / 77 = 79.38961038961 (the remainder is 30, so 77 is not a divisor of 6113)
6113 / 78 = 78.371794871795 (the remainder is 29, so 78 is not a divisor of 6113)