What are the divisors of 4966?

1, 2, 13, 26, 191, 382, 2483, 4966

There is a total of 8 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 1008.

4 even divisors

2, 26, 382, 4966

4 odd divisors

1, 13, 191, 2483

How to compute the divisors of 4966?

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 4966 by each of the numbers from 1 to 4966 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)

4966 / 1 = 4966 (the remainder is 0, so 1 is a divisor of 4966)
4966 / 2 = 2483 (the remainder is 0, so 2 is a divisor of 4966)
4966 / 3 = 1655.3333333333 (the remainder is 1, so 3 is not a divisor of 4966)
...
4966 / 4965 = 1.0002014098691 (the remainder is 1, so 4965 is not a divisor of 4966)
4966 / 4966 = 1 (the remainder is 0, so 4966 is a divisor of 4966)

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 4966 (i.e. 70.469851709791). 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 $\frac{N}{d} = D$ )

4966 / 1 = 4966 (the remainder is 0, so 1 and 4966 are divisors of 4966)
4966 / 2 = 2483 (the remainder is 0, so 2 and 2483 are divisors of 4966)
4966 / 3 = 1655.3333333333 (the remainder is 1, so 3 is not a divisor of 4966)
...
4966 / 69 = 71.971014492754 (the remainder is 67, so 69 is not a divisor of 4966)
4966 / 70 = 70.942857142857 (the remainder is 66, so 70 is not a divisor of 4966)