What are the divisors of 4862?

1, 2, 11, 13, 17, 22, 26, 34, 143, 187, 221, 286, 374, 442, 2431, 4862

There is a total of 16 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 567.

8 even divisors

2, 22, 26, 34, 286, 374, 442, 4862

8 odd divisors

1, 11, 13, 17, 143, 187, 221, 2431

How to compute the divisors of 4862?

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 4862 by each of the numbers from 1 to 4862 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)

4862 / 1 = 4862 (the remainder is 0, so 1 is a divisor of 4862)
4862 / 2 = 2431 (the remainder is 0, so 2 is a divisor of 4862)
4862 / 3 = 1620.6666666667 (the remainder is 2, so 3 is not a divisor of 4862)
...
4862 / 4861 = 1.0002057189879 (the remainder is 1, so 4861 is not a divisor of 4862)
4862 / 4862 = 1 (the remainder is 0, so 4862 is a divisor of 4862)

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 4862 (i.e. 69.728043139041). 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 $\frac{N}{d} = D$ )

4862 / 1 = 4862 (the remainder is 0, so 1 and 4862 are divisors of 4862)
4862 / 2 = 2431 (the remainder is 0, so 2 and 2431 are divisors of 4862)
4862 / 3 = 1620.6666666667 (the remainder is 2, so 3 is not a divisor of 4862)
...
4862 / 68 = 71.5 (the remainder is 34, so 68 is not a divisor of 4862)
4862 / 69 = 70.463768115942 (the remainder is 32, so 69 is not a divisor of 4862)