What are the divisors of 4751?

1, 4751

There is a total of 2 positive divisors.
The sum of these divisors is 4752.
The arithmetic mean is 2376.

2 odd divisors

1, 4751

How to compute the divisors of 4751?

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 4751 by each of the numbers from 1 to 4751 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)

4751 / 1 = 4751 (the remainder is 0, so 1 is a divisor of 4751)
4751 / 2 = 2375.5 (the remainder is 1, so 2 is not a divisor of 4751)
4751 / 3 = 1583.6666666667 (the remainder is 2, so 3 is not a divisor of 4751)
...
4751 / 4750 = 1.0002105263158 (the remainder is 1, so 4750 is not a divisor of 4751)
4751 / 4751 = 1 (the remainder is 0, so 4751 is a divisor of 4751)

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 4751 (i.e. 68.927498141163). 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 $\frac{N}{d} = D$ )

4751 / 1 = 4751 (the remainder is 0, so 1 and 4751 are divisors of 4751)
4751 / 2 = 2375.5 (the remainder is 1, so 2 is not a divisor of 4751)
4751 / 3 = 1583.6666666667 (the remainder is 2, so 3 is not a divisor of 4751)
...
4751 / 67 = 70.910447761194 (the remainder is 61, so 67 is not a divisor of 4751)
4751 / 68 = 69.867647058824 (the remainder is 59, so 68 is not a divisor of 4751)