What are the divisors of 2478?

1, 2, 3, 6, 7, 14, 21, 42, 59, 118, 177, 354, 413, 826, 1239, 2478

There is a total of 16 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 360.

8 even divisors

2, 6, 14, 42, 118, 354, 826, 2478

8 odd divisors

1, 3, 7, 21, 59, 177, 413, 1239

How to compute the divisors of 2478?

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 2478 by each of the numbers from 1 to 2478 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)

2478 / 1 = 2478 (the remainder is 0, so 1 is a divisor of 2478)
2478 / 2 = 1239 (the remainder is 0, so 2 is a divisor of 2478)
2478 / 3 = 826 (the remainder is 0, so 3 is a divisor of 2478)
...
2478 / 2477 = 1.0004037141704 (the remainder is 1, so 2477 is not a divisor of 2478)
2478 / 2478 = 1 (the remainder is 0, so 2478 is a divisor of 2478)

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 2478 (i.e. 49.779513858615). 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 $\frac{N}{d} = D$ )

2478 / 1 = 2478 (the remainder is 0, so 1 and 2478 are divisors of 2478)
2478 / 2 = 1239 (the remainder is 0, so 2 and 1239 are divisors of 2478)
2478 / 3 = 826 (the remainder is 0, so 3 and 826 are divisors of 2478)
...
2478 / 48 = 51.625 (the remainder is 30, so 48 is not a divisor of 2478)
2478 / 49 = 50.571428571429 (the remainder is 28, so 49 is not a divisor of 2478)