What are the divisors of 2644?

1, 2, 4, 661, 1322, 2644

There is a total of 6 positive divisors.
The sum of these divisors is 4634.
The arithmetic mean is 772.33333333333.

4 even divisors

2, 4, 1322, 2644

2 odd divisors

1, 661

How to compute the divisors of 2644?

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 2644 by each of the numbers from 1 to 2644 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)

2644 / 1 = 2644 (the remainder is 0, so 1 is a divisor of 2644)
2644 / 2 = 1322 (the remainder is 0, so 2 is a divisor of 2644)
2644 / 3 = 881.33333333333 (the remainder is 1, so 3 is not a divisor of 2644)
...
2644 / 2643 = 1.0003783579266 (the remainder is 1, so 2643 is not a divisor of 2644)
2644 / 2644 = 1 (the remainder is 0, so 2644 is a divisor of 2644)

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 2644 (i.e. 51.41984052873). 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 $\frac{N}{d} = D$ )

2644 / 1 = 2644 (the remainder is 0, so 1 and 2644 are divisors of 2644)
2644 / 2 = 1322 (the remainder is 0, so 2 and 1322 are divisors of 2644)
2644 / 3 = 881.33333333333 (the remainder is 1, so 3 is not a divisor of 2644)
...
2644 / 50 = 52.88 (the remainder is 44, so 50 is not a divisor of 2644)
2644 / 51 = 51.843137254902 (the remainder is 43, so 51 is not a divisor of 2644)