What are the divisors of 4714?

1, 2, 2357, 4714

There is a total of 4 positive divisors.
The sum of these divisors is 7074.
The arithmetic mean is 1768.5.

2 even divisors

2, 4714

2 odd divisors

1, 2357

How to compute the divisors of 4714?

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 4714 by each of the numbers from 1 to 4714 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)

4714 / 1 = 4714 (the remainder is 0, so 1 is a divisor of 4714)
4714 / 2 = 2357 (the remainder is 0, so 2 is a divisor of 4714)
4714 / 3 = 1571.3333333333 (the remainder is 1, so 3 is not a divisor of 4714)
...
4714 / 4713 = 1.0002121790791 (the remainder is 1, so 4713 is not a divisor of 4714)
4714 / 4714 = 1 (the remainder is 0, so 4714 is a divisor of 4714)

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 4714 (i.e. 68.658575575087). 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 $\frac{N}{d} = D$ )

4714 / 1 = 4714 (the remainder is 0, so 1 and 4714 are divisors of 4714)
4714 / 2 = 2357 (the remainder is 0, so 2 and 2357 are divisors of 4714)
4714 / 3 = 1571.3333333333 (the remainder is 1, so 3 is not a divisor of 4714)
...
4714 / 67 = 70.358208955224 (the remainder is 24, so 67 is not a divisor of 4714)
4714 / 68 = 69.323529411765 (the remainder is 22, so 68 is not a divisor of 4714)