What are the divisors of 4894?

1, 2, 2447, 4894

There is a total of 4 positive divisors.
The sum of these divisors is 7344.
The arithmetic mean is 1836.

2 even divisors

2, 4894

2 odd divisors

1, 2447

How to compute the divisors of 4894?

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 4894 by each of the numbers from 1 to 4894 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)

4894 / 1 = 4894 (the remainder is 0, so 1 is a divisor of 4894)
4894 / 2 = 2447 (the remainder is 0, so 2 is a divisor of 4894)
4894 / 3 = 1631.3333333333 (the remainder is 1, so 3 is not a divisor of 4894)
...
4894 / 4893 = 1.0002043735949 (the remainder is 1, so 4893 is not a divisor of 4894)
4894 / 4894 = 1 (the remainder is 0, so 4894 is a divisor of 4894)

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 4894 (i.e. 69.957129729571). 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 $\frac{N}{d} = D$ )

4894 / 1 = 4894 (the remainder is 0, so 1 and 4894 are divisors of 4894)
4894 / 2 = 2447 (the remainder is 0, so 2 and 2447 are divisors of 4894)
4894 / 3 = 1631.3333333333 (the remainder is 1, so 3 is not a divisor of 4894)
...
4894 / 68 = 71.970588235294 (the remainder is 66, so 68 is not a divisor of 4894)
4894 / 69 = 70.927536231884 (the remainder is 64, so 69 is not a divisor of 4894)