What are the divisors of 4867?

1, 31, 157, 4867

There is a total of 4 positive divisors.
The sum of these divisors is 5056.
The arithmetic mean is 1264.

4 odd divisors

1, 31, 157, 4867

How to compute the divisors of 4867?

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 4867 by each of the numbers from 1 to 4867 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)

4867 / 1 = 4867 (the remainder is 0, so 1 is a divisor of 4867)
4867 / 2 = 2433.5 (the remainder is 1, so 2 is not a divisor of 4867)
4867 / 3 = 1622.3333333333 (the remainder is 1, so 3 is not a divisor of 4867)
...
4867 / 4866 = 1.0002055076038 (the remainder is 1, so 4866 is not a divisor of 4867)
4867 / 4867 = 1 (the remainder is 0, so 4867 is a divisor of 4867)

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 4867 (i.e. 69.76388750636). 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 $\frac{N}{d} = D$ )

4867 / 1 = 4867 (the remainder is 0, so 1 and 4867 are divisors of 4867)
4867 / 2 = 2433.5 (the remainder is 1, so 2 is not a divisor of 4867)
4867 / 3 = 1622.3333333333 (the remainder is 1, so 3 is not a divisor of 4867)
...
4867 / 68 = 71.573529411765 (the remainder is 39, so 68 is not a divisor of 4867)
4867 / 69 = 70.536231884058 (the remainder is 37, so 69 is not a divisor of 4867)