What are the divisors of 2572?

1, 2, 4, 643, 1286, 2572

There is a total of 6 positive divisors.
The sum of these divisors is 4508.
The arithmetic mean is 751.33333333333.

4 even divisors

2, 4, 1286, 2572

2 odd divisors

1, 643

How to compute the divisors of 2572?

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 2572 by each of the numbers from 1 to 2572 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)

2572 / 1 = 2572 (the remainder is 0, so 1 is a divisor of 2572)
2572 / 2 = 1286 (the remainder is 0, so 2 is a divisor of 2572)
2572 / 3 = 857.33333333333 (the remainder is 1, so 3 is not a divisor of 2572)
...
2572 / 2571 = 1.0003889537145 (the remainder is 1, so 2571 is not a divisor of 2572)
2572 / 2572 = 1 (the remainder is 0, so 2572 is a divisor of 2572)

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 2572 (i.e. 50.714889332424). 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 $\frac{N}{d} = D$ )

2572 / 1 = 2572 (the remainder is 0, so 1 and 2572 are divisors of 2572)
2572 / 2 = 1286 (the remainder is 0, so 2 and 1286 are divisors of 2572)
2572 / 3 = 857.33333333333 (the remainder is 1, so 3 is not a divisor of 2572)
...
2572 / 49 = 52.489795918367 (the remainder is 24, so 49 is not a divisor of 2572)
2572 / 50 = 51.44 (the remainder is 22, so 50 is not a divisor of 2572)