What are the divisors of 4801?

1, 4801

There is a total of 2 positive divisors.
The sum of these divisors is 4802.
The arithmetic mean is 2401.

2 odd divisors

1, 4801

How to compute the divisors of 4801?

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 4801 by each of the numbers from 1 to 4801 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)

4801 / 1 = 4801 (the remainder is 0, so 1 is a divisor of 4801)
4801 / 2 = 2400.5 (the remainder is 1, so 2 is not a divisor of 4801)
4801 / 3 = 1600.3333333333 (the remainder is 1, so 3 is not a divisor of 4801)
...
4801 / 4800 = 1.0002083333333 (the remainder is 1, so 4800 is not a divisor of 4801)
4801 / 4801 = 1 (the remainder is 0, so 4801 is a divisor of 4801)

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 4801 (i.e. 69.28924880528). 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 $\frac{N}{d} = D$ )

4801 / 1 = 4801 (the remainder is 0, so 1 and 4801 are divisors of 4801)
4801 / 2 = 2400.5 (the remainder is 1, so 2 is not a divisor of 4801)
4801 / 3 = 1600.3333333333 (the remainder is 1, so 3 is not a divisor of 4801)
...
4801 / 68 = 70.602941176471 (the remainder is 41, so 68 is not a divisor of 4801)
4801 / 69 = 69.579710144928 (the remainder is 40, so 69 is not a divisor of 4801)