What are the divisors of 2862?

1, 2, 3, 6, 9, 18, 27, 53, 54, 106, 159, 318, 477, 954, 1431, 2862

There is a total of 16 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 405.

8 even divisors

2, 6, 18, 54, 106, 318, 954, 2862

8 odd divisors

1, 3, 9, 27, 53, 159, 477, 1431

How to compute the divisors of 2862?

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 2862 by each of the numbers from 1 to 2862 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)

2862 / 1 = 2862 (the remainder is 0, so 1 is a divisor of 2862)
2862 / 2 = 1431 (the remainder is 0, so 2 is a divisor of 2862)
2862 / 3 = 954 (the remainder is 0, so 3 is a divisor of 2862)
...
2862 / 2861 = 1.000349528137 (the remainder is 1, so 2861 is not a divisor of 2862)
2862 / 2862 = 1 (the remainder is 0, so 2862 is a divisor of 2862)

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 2862 (i.e. 53.497663500381). 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 $\frac{N}{d} = D$ )

2862 / 1 = 2862 (the remainder is 0, so 1 and 2862 are divisors of 2862)
2862 / 2 = 1431 (the remainder is 0, so 2 and 1431 are divisors of 2862)
2862 / 3 = 954 (the remainder is 0, so 3 and 954 are divisors of 2862)
...
2862 / 52 = 55.038461538462 (the remainder is 2, so 52 is not a divisor of 2862)
2862 / 53 = 54 (the remainder is 0, so 53 and 54 are divisors of 2862)