What are the divisors of 4701?

1, 3, 1567, 4701

There is a total of 4 positive divisors.
The sum of these divisors is 6272.
The arithmetic mean is 1568.

4 odd divisors

1, 3, 1567, 4701

How to compute the divisors of 4701?

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 4701 by each of the numbers from 1 to 4701 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)

4701 / 1 = 4701 (the remainder is 0, so 1 is a divisor of 4701)
4701 / 2 = 2350.5 (the remainder is 1, so 2 is not a divisor of 4701)
4701 / 3 = 1567 (the remainder is 0, so 3 is a divisor of 4701)
...
4701 / 4700 = 1.0002127659574 (the remainder is 1, so 4700 is not a divisor of 4701)
4701 / 4701 = 1 (the remainder is 0, so 4701 is a divisor of 4701)

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 4701 (i.e. 68.563838865688). 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 $\frac{N}{d} = D$ )

4701 / 1 = 4701 (the remainder is 0, so 1 and 4701 are divisors of 4701)
4701 / 2 = 2350.5 (the remainder is 1, so 2 is not a divisor of 4701)
4701 / 3 = 1567 (the remainder is 0, so 3 and 1567 are divisors of 4701)
...
4701 / 67 = 70.164179104478 (the remainder is 11, so 67 is not a divisor of 4701)
4701 / 68 = 69.132352941176 (the remainder is 9, so 68 is not a divisor of 4701)