What are the divisors of 4934?

1, 2, 2467, 4934

There is a total of 4 positive divisors.
The sum of these divisors is 7404.
The arithmetic mean is 1851.

2 even divisors

2, 4934

2 odd divisors

1, 2467

How to compute the divisors of 4934?

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 4934 by each of the numbers from 1 to 4934 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)

4934 / 1 = 4934 (the remainder is 0, so 1 is a divisor of 4934)
4934 / 2 = 2467 (the remainder is 0, so 2 is a divisor of 4934)
4934 / 3 = 1644.6666666667 (the remainder is 2, so 3 is not a divisor of 4934)
...
4934 / 4933 = 1.0002027163998 (the remainder is 1, so 4933 is not a divisor of 4934)
4934 / 4934 = 1 (the remainder is 0, so 4934 is a divisor of 4934)

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 4934 (i.e. 70.242437315344). 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 $\frac{N}{d} = D$ )

4934 / 1 = 4934 (the remainder is 0, so 1 and 4934 are divisors of 4934)
4934 / 2 = 2467 (the remainder is 0, so 2 and 2467 are divisors of 4934)
4934 / 3 = 1644.6666666667 (the remainder is 2, so 3 is not a divisor of 4934)
...
4934 / 69 = 71.507246376812 (the remainder is 35, so 69 is not a divisor of 4934)
4934 / 70 = 70.485714285714 (the remainder is 34, so 70 is not a divisor of 4934)