What are the divisors of 2833?

1, 2833

There is a total of 2 positive divisors.
The sum of these divisors is 2834.
The arithmetic mean is 1417.

2 odd divisors

1, 2833

How to compute the divisors of 2833?

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 2833 by each of the numbers from 1 to 2833 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)

2833 / 1 = 2833 (the remainder is 0, so 1 is a divisor of 2833)
2833 / 2 = 1416.5 (the remainder is 1, so 2 is not a divisor of 2833)
2833 / 3 = 944.33333333333 (the remainder is 1, so 3 is not a divisor of 2833)
...
2833 / 2832 = 1.0003531073446 (the remainder is 1, so 2832 is not a divisor of 2833)
2833 / 2833 = 1 (the remainder is 0, so 2833 is a divisor of 2833)

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 2833 (i.e. 53.225933528685). 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 $\frac{N}{d} = D$ )

2833 / 1 = 2833 (the remainder is 0, so 1 and 2833 are divisors of 2833)
2833 / 2 = 1416.5 (the remainder is 1, so 2 is not a divisor of 2833)
2833 / 3 = 944.33333333333 (the remainder is 1, so 3 is not a divisor of 2833)
...
2833 / 52 = 54.480769230769 (the remainder is 25, so 52 is not a divisor of 2833)
2833 / 53 = 53.452830188679 (the remainder is 24, so 53 is not a divisor of 2833)