What are the divisors of 4693?

1, 13, 19, 247, 361, 4693

There is a total of 6 positive divisors.
The sum of these divisors is 5334.
The arithmetic mean is 889.

6 odd divisors

1, 13, 19, 247, 361, 4693

How to compute the divisors of 4693?

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 4693 by each of the numbers from 1 to 4693 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)

4693 / 1 = 4693 (the remainder is 0, so 1 is a divisor of 4693)
4693 / 2 = 2346.5 (the remainder is 1, so 2 is not a divisor of 4693)
4693 / 3 = 1564.3333333333 (the remainder is 1, so 3 is not a divisor of 4693)
...
4693 / 4692 = 1.0002131287298 (the remainder is 1, so 4692 is not a divisor of 4693)
4693 / 4693 = 1 (the remainder is 0, so 4693 is a divisor of 4693)

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 4693 (i.e. 68.505474233816). 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 $\frac{N}{d} = D$ )

4693 / 1 = 4693 (the remainder is 0, so 1 and 4693 are divisors of 4693)
4693 / 2 = 2346.5 (the remainder is 1, so 2 is not a divisor of 4693)
4693 / 3 = 1564.3333333333 (the remainder is 1, so 3 is not a divisor of 4693)
...
4693 / 67 = 70.044776119403 (the remainder is 3, so 67 is not a divisor of 4693)
4693 / 68 = 69.014705882353 (the remainder is 1, so 68 is not a divisor of 4693)