What are the divisors of 2485?

1, 5, 7, 35, 71, 355, 497, 2485

There is a total of 8 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 432.

8 odd divisors

1, 5, 7, 35, 71, 355, 497, 2485

How to compute the divisors of 2485?

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 2485 by each of the numbers from 1 to 2485 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)

2485 / 1 = 2485 (the remainder is 0, so 1 is a divisor of 2485)
2485 / 2 = 1242.5 (the remainder is 1, so 2 is not a divisor of 2485)
2485 / 3 = 828.33333333333 (the remainder is 1, so 3 is not a divisor of 2485)
...
2485 / 2484 = 1.0004025764895 (the remainder is 1, so 2484 is not a divisor of 2485)
2485 / 2485 = 1 (the remainder is 0, so 2485 is a divisor of 2485)

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 2485 (i.e. 49.849774322458). 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 $\frac{N}{d} = D$ )

2485 / 1 = 2485 (the remainder is 0, so 1 and 2485 are divisors of 2485)
2485 / 2 = 1242.5 (the remainder is 1, so 2 is not a divisor of 2485)
2485 / 3 = 828.33333333333 (the remainder is 1, so 3 is not a divisor of 2485)
...
2485 / 48 = 51.770833333333 (the remainder is 37, so 48 is not a divisor of 2485)
2485 / 49 = 50.714285714286 (the remainder is 35, so 49 is not a divisor of 2485)