What are the divisors of 2479?

1, 37, 67, 2479

There is a total of 4 positive divisors.
The sum of these divisors is 2584.
The arithmetic mean is 646.

4 odd divisors

1, 37, 67, 2479

How to compute the divisors of 2479?

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 2479 by each of the numbers from 1 to 2479 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)

2479 / 1 = 2479 (the remainder is 0, so 1 is a divisor of 2479)
2479 / 2 = 1239.5 (the remainder is 1, so 2 is not a divisor of 2479)
2479 / 3 = 826.33333333333 (the remainder is 1, so 3 is not a divisor of 2479)
...
2479 / 2478 = 1.000403551251 (the remainder is 1, so 2478 is not a divisor of 2479)
2479 / 2479 = 1 (the remainder is 0, so 2479 is a divisor of 2479)

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 2479 (i.e. 49.789557138018). 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 $\frac{N}{d} = D$ )

2479 / 1 = 2479 (the remainder is 0, so 1 and 2479 are divisors of 2479)
2479 / 2 = 1239.5 (the remainder is 1, so 2 is not a divisor of 2479)
2479 / 3 = 826.33333333333 (the remainder is 1, so 3 is not a divisor of 2479)
...
2479 / 48 = 51.645833333333 (the remainder is 31, so 48 is not a divisor of 2479)
2479 / 49 = 50.591836734694 (the remainder is 29, so 49 is not a divisor of 2479)