What are the divisors of 2966?

1, 2, 1483, 2966

There is a total of 4 positive divisors.
The sum of these divisors is 4452.
The arithmetic mean is 1113.

2 even divisors

2, 2966

2 odd divisors

1, 1483

How to compute the divisors of 2966?

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 2966 by each of the numbers from 1 to 2966 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)

2966 / 1 = 2966 (the remainder is 0, so 1 is a divisor of 2966)
2966 / 2 = 1483 (the remainder is 0, so 2 is a divisor of 2966)
2966 / 3 = 988.66666666667 (the remainder is 2, so 3 is not a divisor of 2966)
...
2966 / 2965 = 1.0003372681282 (the remainder is 1, so 2965 is not a divisor of 2966)
2966 / 2966 = 1 (the remainder is 0, so 2966 is a divisor of 2966)

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 2966 (i.e. 54.46099521676). 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 $\frac{N}{d} = D$ )

2966 / 1 = 2966 (the remainder is 0, so 1 and 2966 are divisors of 2966)
2966 / 2 = 1483 (the remainder is 0, so 2 and 1483 are divisors of 2966)
2966 / 3 = 988.66666666667 (the remainder is 2, so 3 is not a divisor of 2966)
...
2966 / 53 = 55.962264150943 (the remainder is 51, so 53 is not a divisor of 2966)
2966 / 54 = 54.925925925926 (the remainder is 50, so 54 is not a divisor of 2966)