What are the divisors of 6145?

1, 5, 1229, 6145

There is a total of 4 positive divisors.
The sum of these divisors is 7380.
The arithmetic mean is 1845.

4 odd divisors

1, 5, 1229, 6145

How to compute the divisors of 6145?

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 6145 by each of the numbers from 1 to 6145 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)

6145 / 1 = 6145 (the remainder is 0, so 1 is a divisor of 6145)
6145 / 2 = 3072.5 (the remainder is 1, so 2 is not a divisor of 6145)
6145 / 3 = 2048.3333333333 (the remainder is 1, so 3 is not a divisor of 6145)
...
6145 / 6144 = 1.0001627604167 (the remainder is 1, so 6144 is not a divisor of 6145)
6145 / 6145 = 1 (the remainder is 0, so 6145 is a divisor of 6145)

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 6145 (i.e. 78.390050389064). 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 $\frac{N}{d} = D$ )

6145 / 1 = 6145 (the remainder is 0, so 1 and 6145 are divisors of 6145)
6145 / 2 = 3072.5 (the remainder is 1, so 2 is not a divisor of 6145)
6145 / 3 = 2048.3333333333 (the remainder is 1, so 3 is not a divisor of 6145)
...
6145 / 77 = 79.805194805195 (the remainder is 62, so 77 is not a divisor of 6145)
6145 / 78 = 78.782051282051 (the remainder is 61, so 78 is not a divisor of 6145)