What are the divisors of 2464?

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 56, 77, 88, 112, 154, 176, 224, 308, 352, 616, 1232, 2464

There is a total of 24 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 252.

20 even divisors

2, 4, 8, 14, 16, 22, 28, 32, 44, 56, 88, 112, 154, 176, 224, 308, 352, 616, 1232, 2464

4 odd divisors

1, 7, 11, 77

How to compute the divisors of 2464?

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 2464 by each of the numbers from 1 to 2464 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)

2464 / 1 = 2464 (the remainder is 0, so 1 is a divisor of 2464)
2464 / 2 = 1232 (the remainder is 0, so 2 is a divisor of 2464)
2464 / 3 = 821.33333333333 (the remainder is 1, so 3 is not a divisor of 2464)
...
2464 / 2463 = 1.0004060089322 (the remainder is 1, so 2463 is not a divisor of 2464)
2464 / 2464 = 1 (the remainder is 0, so 2464 is a divisor of 2464)

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 2464 (i.e. 49.638694583963). 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 $\frac{N}{d} = D$ )

2464 / 1 = 2464 (the remainder is 0, so 1 and 2464 are divisors of 2464)
2464 / 2 = 1232 (the remainder is 0, so 2 and 1232 are divisors of 2464)
2464 / 3 = 821.33333333333 (the remainder is 1, so 3 is not a divisor of 2464)
...
2464 / 48 = 51.333333333333 (the remainder is 16, so 48 is not a divisor of 2464)
2464 / 49 = 50.285714285714 (the remainder is 14, so 49 is not a divisor of 2464)