What are the divisors of 4982?

1, 2, 47, 53, 94, 106, 2491, 4982

There is a total of 8 positive divisors.
The sum of these divisors is 7776.
The arithmetic mean is 972.

4 even divisors

2, 94, 106, 4982

4 odd divisors

1, 47, 53, 2491

How to compute the divisors of 4982?

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 4982 by each of the numbers from 1 to 4982 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)

4982 / 1 = 4982 (the remainder is 0, so 1 is a divisor of 4982)
4982 / 2 = 2491 (the remainder is 0, so 2 is a divisor of 4982)
4982 / 3 = 1660.6666666667 (the remainder is 2, so 3 is not a divisor of 4982)
...
4982 / 4981 = 1.000200762899 (the remainder is 1, so 4981 is not a divisor of 4982)
4982 / 4982 = 1 (the remainder is 0, so 4982 is a divisor of 4982)

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 4982 (i.e. 70.583284140085). 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 $\frac{N}{d} = D$ )

4982 / 1 = 4982 (the remainder is 0, so 1 and 4982 are divisors of 4982)
4982 / 2 = 2491 (the remainder is 0, so 2 and 2491 are divisors of 4982)
4982 / 3 = 1660.6666666667 (the remainder is 2, so 3 is not a divisor of 4982)
...
4982 / 69 = 72.202898550725 (the remainder is 14, so 69 is not a divisor of 4982)
4982 / 70 = 71.171428571429 (the remainder is 12, so 70 is not a divisor of 4982)