What are the divisors of 4713?

1, 3, 1571, 4713

There is a total of 4 positive divisors.
The sum of these divisors is 6288.
The arithmetic mean is 1572.

4 odd divisors

1, 3, 1571, 4713

How to compute the divisors of 4713?

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 4713 by each of the numbers from 1 to 4713 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)

4713 / 1 = 4713 (the remainder is 0, so 1 is a divisor of 4713)
4713 / 2 = 2356.5 (the remainder is 1, so 2 is not a divisor of 4713)
4713 / 3 = 1571 (the remainder is 0, so 3 is a divisor of 4713)
...
4713 / 4712 = 1.0002122241087 (the remainder is 1, so 4712 is not a divisor of 4713)
4713 / 4713 = 1 (the remainder is 0, so 4713 is a divisor of 4713)

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 4713 (i.e. 68.65129277734). 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 $\frac{N}{d} = D$ )

4713 / 1 = 4713 (the remainder is 0, so 1 and 4713 are divisors of 4713)
4713 / 2 = 2356.5 (the remainder is 1, so 2 is not a divisor of 4713)
4713 / 3 = 1571 (the remainder is 0, so 3 and 1571 are divisors of 4713)
...
4713 / 67 = 70.34328358209 (the remainder is 23, so 67 is not a divisor of 4713)
4713 / 68 = 69.308823529412 (the remainder is 21, so 68 is not a divisor of 4713)