What are the divisors of 2725?

1, 5, 25, 109, 545, 2725

There is a total of 6 positive divisors.
The sum of these divisors is 3410.
The arithmetic mean is 568.33333333333.

6 odd divisors

1, 5, 25, 109, 545, 2725

How to compute the divisors of 2725?

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 2725 by each of the numbers from 1 to 2725 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)

2725 / 1 = 2725 (the remainder is 0, so 1 is a divisor of 2725)
2725 / 2 = 1362.5 (the remainder is 1, so 2 is not a divisor of 2725)
2725 / 3 = 908.33333333333 (the remainder is 1, so 3 is not a divisor of 2725)
...
2725 / 2724 = 1.0003671071953 (the remainder is 1, so 2724 is not a divisor of 2725)
2725 / 2725 = 1 (the remainder is 0, so 2725 is a divisor of 2725)

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 2725 (i.e. 52.201532544553). 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 $\frac{N}{d} = D$ )

2725 / 1 = 2725 (the remainder is 0, so 1 and 2725 are divisors of 2725)
2725 / 2 = 1362.5 (the remainder is 1, so 2 is not a divisor of 2725)
2725 / 3 = 908.33333333333 (the remainder is 1, so 3 is not a divisor of 2725)
...
2725 / 51 = 53.43137254902 (the remainder is 22, so 51 is not a divisor of 2725)
2725 / 52 = 52.403846153846 (the remainder is 21, so 52 is not a divisor of 2725)