What are the divisors of 2854?

1, 2, 1427, 2854

There is a total of 4 positive divisors.
The sum of these divisors is 4284.
The arithmetic mean is 1071.

2 even divisors

2, 2854

2 odd divisors

1, 1427

How to compute the divisors of 2854?

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 2854 by each of the numbers from 1 to 2854 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)

2854 / 1 = 2854 (the remainder is 0, so 1 is a divisor of 2854)
2854 / 2 = 1427 (the remainder is 0, so 2 is a divisor of 2854)
2854 / 3 = 951.33333333333 (the remainder is 1, so 3 is not a divisor of 2854)
...
2854 / 2853 = 1.0003505082369 (the remainder is 1, so 2853 is not a divisor of 2854)
2854 / 2854 = 1 (the remainder is 0, so 2854 is a divisor of 2854)

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 2854 (i.e. 53.422841556772). 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 $\frac{N}{d} = D$ )

2854 / 1 = 2854 (the remainder is 0, so 1 and 2854 are divisors of 2854)
2854 / 2 = 1427 (the remainder is 0, so 2 and 1427 are divisors of 2854)
2854 / 3 = 951.33333333333 (the remainder is 1, so 3 is not a divisor of 2854)
...
2854 / 52 = 54.884615384615 (the remainder is 46, so 52 is not a divisor of 2854)
2854 / 53 = 53.849056603774 (the remainder is 45, so 53 is not a divisor of 2854)