What are the divisors of 4846?

1, 2, 2423, 4846

There is a total of 4 positive divisors.
The sum of these divisors is 7272.
The arithmetic mean is 1818.

2 even divisors

2, 4846

2 odd divisors

1, 2423

How to compute the divisors of 4846?

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 4846 by each of the numbers from 1 to 4846 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)

4846 / 1 = 4846 (the remainder is 0, so 1 is a divisor of 4846)
4846 / 2 = 2423 (the remainder is 0, so 2 is a divisor of 4846)
4846 / 3 = 1615.3333333333 (the remainder is 1, so 3 is not a divisor of 4846)
...
4846 / 4845 = 1.0002063983488 (the remainder is 1, so 4845 is not a divisor of 4846)
4846 / 4846 = 1 (the remainder is 0, so 4846 is a divisor of 4846)

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 4846 (i.e. 69.613217135828). 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 $\frac{N}{d} = D$ )

4846 / 1 = 4846 (the remainder is 0, so 1 and 4846 are divisors of 4846)
4846 / 2 = 2423 (the remainder is 0, so 2 and 2423 are divisors of 4846)
4846 / 3 = 1615.3333333333 (the remainder is 1, so 3 is not a divisor of 4846)
...
4846 / 68 = 71.264705882353 (the remainder is 18, so 68 is not a divisor of 4846)
4846 / 69 = 70.231884057971 (the remainder is 16, so 69 is not a divisor of 4846)