What are the divisors of 2573?

1, 31, 83, 2573

There is a total of 4 positive divisors.
The sum of these divisors is 2688.
The arithmetic mean is 672.

4 odd divisors

1, 31, 83, 2573

How to compute the divisors of 2573?

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 2573 by each of the numbers from 1 to 2573 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)

2573 / 1 = 2573 (the remainder is 0, so 1 is a divisor of 2573)
2573 / 2 = 1286.5 (the remainder is 1, so 2 is not a divisor of 2573)
2573 / 3 = 857.66666666667 (the remainder is 2, so 3 is not a divisor of 2573)
...
2573 / 2572 = 1.0003888024883 (the remainder is 1, so 2572 is not a divisor of 2573)
2573 / 2573 = 1 (the remainder is 0, so 2573 is a divisor of 2573)

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 2573 (i.e. 50.72474741189). 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 $\frac{N}{d} = D$ )

2573 / 1 = 2573 (the remainder is 0, so 1 and 2573 are divisors of 2573)
2573 / 2 = 1286.5 (the remainder is 1, so 2 is not a divisor of 2573)
2573 / 3 = 857.66666666667 (the remainder is 2, so 3 is not a divisor of 2573)
...
2573 / 49 = 52.510204081633 (the remainder is 25, so 49 is not a divisor of 2573)
2573 / 50 = 51.46 (the remainder is 23, so 50 is not a divisor of 2573)