What are the divisors of 4858?

1, 2, 7, 14, 347, 694, 2429, 4858

There is a total of 8 positive divisors.
The sum of these divisors is 8352.
The arithmetic mean is 1044.

4 even divisors

2, 14, 694, 4858

4 odd divisors

1, 7, 347, 2429

How to compute the divisors of 4858?

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 4858 by each of the numbers from 1 to 4858 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)

4858 / 1 = 4858 (the remainder is 0, so 1 is a divisor of 4858)
4858 / 2 = 2429 (the remainder is 0, so 2 is a divisor of 4858)
4858 / 3 = 1619.3333333333 (the remainder is 1, so 3 is not a divisor of 4858)
...
4858 / 4857 = 1.0002058884085 (the remainder is 1, so 4857 is not a divisor of 4858)
4858 / 4858 = 1 (the remainder is 0, so 4858 is a divisor of 4858)

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 4858 (i.e. 69.699354372906). 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 $\frac{N}{d} = D$ )

4858 / 1 = 4858 (the remainder is 0, so 1 and 4858 are divisors of 4858)
4858 / 2 = 2429 (the remainder is 0, so 2 and 2429 are divisors of 4858)
4858 / 3 = 1619.3333333333 (the remainder is 1, so 3 is not a divisor of 4858)
...
4858 / 68 = 71.441176470588 (the remainder is 30, so 68 is not a divisor of 4858)
4858 / 69 = 70.405797101449 (the remainder is 28, so 69 is not a divisor of 4858)