What are the divisors of 2893?

1, 11, 263, 2893

There is a total of 4 positive divisors.
The sum of these divisors is 3168.
The arithmetic mean is 792.

4 odd divisors

1, 11, 263, 2893

How to compute the divisors of 2893?

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 2893 by each of the numbers from 1 to 2893 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)

2893 / 1 = 2893 (the remainder is 0, so 1 is a divisor of 2893)
2893 / 2 = 1446.5 (the remainder is 1, so 2 is not a divisor of 2893)
2893 / 3 = 964.33333333333 (the remainder is 1, so 3 is not a divisor of 2893)
...
2893 / 2892 = 1.0003457814661 (the remainder is 1, so 2892 is not a divisor of 2893)
2893 / 2893 = 1 (the remainder is 0, so 2893 is a divisor of 2893)

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 2893 (i.e. 53.786615435441). 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 $\frac{N}{d} = D$ )

2893 / 1 = 2893 (the remainder is 0, so 1 and 2893 are divisors of 2893)
2893 / 2 = 1446.5 (the remainder is 1, so 2 is not a divisor of 2893)
2893 / 3 = 964.33333333333 (the remainder is 1, so 3 is not a divisor of 2893)
...
2893 / 52 = 55.634615384615 (the remainder is 33, so 52 is not a divisor of 2893)
2893 / 53 = 54.584905660377 (the remainder is 31, so 53 is not a divisor of 2893)