What are the divisors of 4745?

1, 5, 13, 65, 73, 365, 949, 4745

There is a total of 8 positive divisors.
The sum of these divisors is 6216.
The arithmetic mean is 777.

8 odd divisors

1, 5, 13, 65, 73, 365, 949, 4745

How to compute the divisors of 4745?

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 4745 by each of the numbers from 1 to 4745 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)

4745 / 1 = 4745 (the remainder is 0, so 1 is a divisor of 4745)
4745 / 2 = 2372.5 (the remainder is 1, so 2 is not a divisor of 4745)
4745 / 3 = 1581.6666666667 (the remainder is 2, so 3 is not a divisor of 4745)
...
4745 / 4744 = 1.0002107925801 (the remainder is 1, so 4744 is not a divisor of 4745)
4745 / 4745 = 1 (the remainder is 0, so 4745 is a divisor of 4745)

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 4745 (i.e. 68.883960397178). 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 $\frac{N}{d} = D$ )

4745 / 1 = 4745 (the remainder is 0, so 1 and 4745 are divisors of 4745)
4745 / 2 = 2372.5 (the remainder is 1, so 2 is not a divisor of 4745)
4745 / 3 = 1581.6666666667 (the remainder is 2, so 3 is not a divisor of 4745)
...
4745 / 67 = 70.820895522388 (the remainder is 55, so 67 is not a divisor of 4745)
4745 / 68 = 69.779411764706 (the remainder is 53, so 68 is not a divisor of 4745)