What are the divisors of 2470?

1, 2, 5, 10, 13, 19, 26, 38, 65, 95, 130, 190, 247, 494, 1235, 2470

There is a total of 16 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 315.

8 even divisors

2, 10, 26, 38, 130, 190, 494, 2470

8 odd divisors

1, 5, 13, 19, 65, 95, 247, 1235

How to compute the divisors of 2470?

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 2470 by each of the numbers from 1 to 2470 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)

2470 / 1 = 2470 (the remainder is 0, so 1 is a divisor of 2470)
2470 / 2 = 1235 (the remainder is 0, so 2 is a divisor of 2470)
2470 / 3 = 823.33333333333 (the remainder is 1, so 3 is not a divisor of 2470)
...
2470 / 2469 = 1.0004050222762 (the remainder is 1, so 2469 is not a divisor of 2470)
2470 / 2470 = 1 (the remainder is 0, so 2470 is a divisor of 2470)

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 2470 (i.e. 49.699094559157). 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 $\frac{N}{d} = D$ )

2470 / 1 = 2470 (the remainder is 0, so 1 and 2470 are divisors of 2470)
2470 / 2 = 1235 (the remainder is 0, so 2 and 1235 are divisors of 2470)
2470 / 3 = 823.33333333333 (the remainder is 1, so 3 is not a divisor of 2470)
...
2470 / 48 = 51.458333333333 (the remainder is 22, so 48 is not a divisor of 2470)
2470 / 49 = 50.408163265306 (the remainder is 20, so 49 is not a divisor of 2470)