What are the divisors of 4913?

1, 17, 289, 4913

There is a total of 4 positive divisors.
The sum of these divisors is 5220.
The arithmetic mean is 1305.

4 odd divisors

1, 17, 289, 4913

How to compute the divisors of 4913?

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 4913 by each of the numbers from 1 to 4913 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)

4913 / 1 = 4913 (the remainder is 0, so 1 is a divisor of 4913)
4913 / 2 = 2456.5 (the remainder is 1, so 2 is not a divisor of 4913)
4913 / 3 = 1637.6666666667 (the remainder is 2, so 3 is not a divisor of 4913)
...
4913 / 4912 = 1.0002035830619 (the remainder is 1, so 4912 is not a divisor of 4913)
4913 / 4913 = 1 (the remainder is 0, so 4913 is a divisor of 4913)

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 4913 (i.e. 70.0927956355). 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 $\frac{N}{d} = D$ )

4913 / 1 = 4913 (the remainder is 0, so 1 and 4913 are divisors of 4913)
4913 / 2 = 2456.5 (the remainder is 1, so 2 is not a divisor of 4913)
4913 / 3 = 1637.6666666667 (the remainder is 2, so 3 is not a divisor of 4913)
...
4913 / 69 = 71.202898550725 (the remainder is 14, so 69 is not a divisor of 4913)
4913 / 70 = 70.185714285714 (the remainder is 13, so 70 is not a divisor of 4913)