What are the divisors of 2982?

1, 2, 3, 6, 7, 14, 21, 42, 71, 142, 213, 426, 497, 994, 1491, 2982

There is a total of 16 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 432.

8 even divisors

2, 6, 14, 42, 142, 426, 994, 2982

8 odd divisors

1, 3, 7, 21, 71, 213, 497, 1491

How to compute the divisors of 2982?

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 2982 by each of the numbers from 1 to 2982 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)

2982 / 1 = 2982 (the remainder is 0, so 1 is a divisor of 2982)
2982 / 2 = 1491 (the remainder is 0, so 2 is a divisor of 2982)
2982 / 3 = 994 (the remainder is 0, so 3 is a divisor of 2982)
...
2982 / 2981 = 1.0003354579 (the remainder is 1, so 2981 is not a divisor of 2982)
2982 / 2982 = 1 (the remainder is 0, so 2982 is a divisor of 2982)

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 2982 (i.e. 54.607691765904). 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 $\frac{N}{d} = D$ )

2982 / 1 = 2982 (the remainder is 0, so 1 and 2982 are divisors of 2982)
2982 / 2 = 1491 (the remainder is 0, so 2 and 1491 are divisors of 2982)
2982 / 3 = 994 (the remainder is 0, so 3 and 994 are divisors of 2982)
...
2982 / 53 = 56.264150943396 (the remainder is 14, so 53 is not a divisor of 2982)
2982 / 54 = 55.222222222222 (the remainder is 12, so 54 is not a divisor of 2982)