What are the divisors of 4771?

1, 13, 367, 4771

There is a total of 4 positive divisors.
The sum of these divisors is 5152.
The arithmetic mean is 1288.

4 odd divisors

1, 13, 367, 4771

How to compute the divisors of 4771?

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 4771 by each of the numbers from 1 to 4771 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)

4771 / 1 = 4771 (the remainder is 0, so 1 is a divisor of 4771)
4771 / 2 = 2385.5 (the remainder is 1, so 2 is not a divisor of 4771)
4771 / 3 = 1590.3333333333 (the remainder is 1, so 3 is not a divisor of 4771)
...
4771 / 4770 = 1.0002096436059 (the remainder is 1, so 4770 is not a divisor of 4771)
4771 / 4771 = 1 (the remainder is 0, so 4771 is a divisor of 4771)

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 4771 (i.e. 69.072425757316). 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 $\frac{N}{d} = D$ )

4771 / 1 = 4771 (the remainder is 0, so 1 and 4771 are divisors of 4771)
4771 / 2 = 2385.5 (the remainder is 1, so 2 is not a divisor of 4771)
4771 / 3 = 1590.3333333333 (the remainder is 1, so 3 is not a divisor of 4771)
...
4771 / 68 = 70.161764705882 (the remainder is 11, so 68 is not a divisor of 4771)
4771 / 69 = 69.144927536232 (the remainder is 10, so 69 is not a divisor of 4771)