What are the divisors of 2853?

1, 3, 9, 317, 951, 2853

There is a total of 6 positive divisors.
The sum of these divisors is 4134.
The arithmetic mean is 689.

6 odd divisors

1, 3, 9, 317, 951, 2853

How to compute the divisors of 2853?

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 2853 by each of the numbers from 1 to 2853 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)

2853 / 1 = 2853 (the remainder is 0, so 1 is a divisor of 2853)
2853 / 2 = 1426.5 (the remainder is 1, so 2 is not a divisor of 2853)
2853 / 3 = 951 (the remainder is 0, so 3 is a divisor of 2853)
...
2853 / 2852 = 1.000350631136 (the remainder is 1, so 2852 is not a divisor of 2853)
2853 / 2853 = 1 (the remainder is 0, so 2853 is a divisor of 2853)

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 2853 (i.e. 53.413481444295). 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 $\frac{N}{d} = D$ )

2853 / 1 = 2853 (the remainder is 0, so 1 and 2853 are divisors of 2853)
2853 / 2 = 1426.5 (the remainder is 1, so 2 is not a divisor of 2853)
2853 / 3 = 951 (the remainder is 0, so 3 and 951 are divisors of 2853)
...
2853 / 52 = 54.865384615385 (the remainder is 45, so 52 is not a divisor of 2853)
2853 / 53 = 53.830188679245 (the remainder is 44, so 53 is not a divisor of 2853)