What are the divisors of 2894?

1, 2, 1447, 2894

There is a total of 4 positive divisors.
The sum of these divisors is 4344.
The arithmetic mean is 1086.

2 even divisors

2, 2894

2 odd divisors

1, 1447

How to compute the divisors of 2894?

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 2894 by each of the numbers from 1 to 2894 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)

2894 / 1 = 2894 (the remainder is 0, so 1 is a divisor of 2894)
2894 / 2 = 1447 (the remainder is 0, so 2 is a divisor of 2894)
2894 / 3 = 964.66666666667 (the remainder is 2, so 3 is not a divisor of 2894)
...
2894 / 2893 = 1.0003456619426 (the remainder is 1, so 2893 is not a divisor of 2894)
2894 / 2894 = 1 (the remainder is 0, so 2894 is a divisor of 2894)

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 2894 (i.e. 53.795910625251). 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 $\frac{N}{d} = D$ )

2894 / 1 = 2894 (the remainder is 0, so 1 and 2894 are divisors of 2894)
2894 / 2 = 1447 (the remainder is 0, so 2 and 1447 are divisors of 2894)
2894 / 3 = 964.66666666667 (the remainder is 2, so 3 is not a divisor of 2894)
...
2894 / 52 = 55.653846153846 (the remainder is 34, so 52 is not a divisor of 2894)
2894 / 53 = 54.603773584906 (the remainder is 32, so 53 is not a divisor of 2894)