What are the divisors of 6175?

1, 5, 13, 19, 25, 65, 95, 247, 325, 475, 1235, 6175

There is a total of 12 positive divisors.
The sum of these divisors is 8680.
The arithmetic mean is 723.33333333333.

12 odd divisors

1, 5, 13, 19, 25, 65, 95, 247, 325, 475, 1235, 6175

How to compute the divisors of 6175?

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 6175 by each of the numbers from 1 to 6175 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)

6175 / 1 = 6175 (the remainder is 0, so 1 is a divisor of 6175)
6175 / 2 = 3087.5 (the remainder is 1, so 2 is not a divisor of 6175)
6175 / 3 = 2058.3333333333 (the remainder is 1, so 3 is not a divisor of 6175)
...
6175 / 6174 = 1.0001619695497 (the remainder is 1, so 6174 is not a divisor of 6175)
6175 / 6175 = 1 (the remainder is 0, so 6175 is a divisor of 6175)

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 6175 (i.e. 78.581168227509). 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 $\frac{N}{d} = D$ )

6175 / 1 = 6175 (the remainder is 0, so 1 and 6175 are divisors of 6175)
6175 / 2 = 3087.5 (the remainder is 1, so 2 is not a divisor of 6175)
6175 / 3 = 2058.3333333333 (the remainder is 1, so 3 is not a divisor of 6175)
...
6175 / 77 = 80.194805194805 (the remainder is 15, so 77 is not a divisor of 6175)
6175 / 78 = 79.166666666667 (the remainder is 13, so 78 is not a divisor of 6175)