What are the divisors of 6025?

1, 5, 25, 241, 1205, 6025

There is a total of 6 positive divisors.
The sum of these divisors is 7502.
The arithmetic mean is 1250.3333333333.

6 odd divisors

1, 5, 25, 241, 1205, 6025

How to compute the divisors of 6025?

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 6025 by each of the numbers from 1 to 6025 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)

6025 / 1 = 6025 (the remainder is 0, so 1 is a divisor of 6025)
6025 / 2 = 3012.5 (the remainder is 1, so 2 is not a divisor of 6025)
6025 / 3 = 2008.3333333333 (the remainder is 1, so 3 is not a divisor of 6025)
...
6025 / 6024 = 1.000166002656 (the remainder is 1, so 6024 is not a divisor of 6025)
6025 / 6025 = 1 (the remainder is 0, so 6025 is a divisor of 6025)

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 6025 (i.e. 77.6208734813). 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 $\frac{N}{d} = D$ )

6025 / 1 = 6025 (the remainder is 0, so 1 and 6025 are divisors of 6025)
6025 / 2 = 3012.5 (the remainder is 1, so 2 is not a divisor of 6025)
6025 / 3 = 2008.3333333333 (the remainder is 1, so 3 is not a divisor of 6025)
...
6025 / 76 = 79.276315789474 (the remainder is 21, so 76 is not a divisor of 6025)
6025 / 77 = 78.246753246753 (the remainder is 19, so 77 is not a divisor of 6025)