What are the divisors of 4710?

1, 2, 3, 5, 6, 10, 15, 30, 157, 314, 471, 785, 942, 1570, 2355, 4710

There is a total of 16 positive divisors.
The sum of these divisors is 11376.
The arithmetic mean is 711.

8 even divisors

2, 6, 10, 30, 314, 942, 1570, 4710

8 odd divisors

1, 3, 5, 15, 157, 471, 785, 2355

How to compute the divisors of 4710?

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 4710 by each of the numbers from 1 to 4710 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)

4710 / 1 = 4710 (the remainder is 0, so 1 is a divisor of 4710)
4710 / 2 = 2355 (the remainder is 0, so 2 is a divisor of 4710)
4710 / 3 = 1570 (the remainder is 0, so 3 is a divisor of 4710)
...
4710 / 4709 = 1.000212359312 (the remainder is 1, so 4709 is not a divisor of 4710)
4710 / 4710 = 1 (the remainder is 0, so 4710 is a divisor of 4710)

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 4710 (i.e. 68.629439747094). 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 $\frac{N}{d} = D$ )

4710 / 1 = 4710 (the remainder is 0, so 1 and 4710 are divisors of 4710)
4710 / 2 = 2355 (the remainder is 0, so 2 and 2355 are divisors of 4710)
4710 / 3 = 1570 (the remainder is 0, so 3 and 1570 are divisors of 4710)
...
4710 / 67 = 70.298507462687 (the remainder is 20, so 67 is not a divisor of 4710)
4710 / 68 = 69.264705882353 (the remainder is 18, so 68 is not a divisor of 4710)