What are the divisors of 4775?

1, 5, 25, 191, 955, 4775

There is a total of 6 positive divisors.
The sum of these divisors is 5952.
The arithmetic mean is 992.

6 odd divisors

1, 5, 25, 191, 955, 4775

How to compute the divisors of 4775?

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 4775 by each of the numbers from 1 to 4775 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)

4775 / 1 = 4775 (the remainder is 0, so 1 is a divisor of 4775)
4775 / 2 = 2387.5 (the remainder is 1, so 2 is not a divisor of 4775)
4775 / 3 = 1591.6666666667 (the remainder is 2, so 3 is not a divisor of 4775)
...
4775 / 4774 = 1.0002094679514 (the remainder is 1, so 4774 is not a divisor of 4775)
4775 / 4775 = 1 (the remainder is 0, so 4775 is a divisor of 4775)

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 4775 (i.e. 69.101374805426). 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 $\frac{N}{d} = D$ )

4775 / 1 = 4775 (the remainder is 0, so 1 and 4775 are divisors of 4775)
4775 / 2 = 2387.5 (the remainder is 1, so 2 is not a divisor of 4775)
4775 / 3 = 1591.6666666667 (the remainder is 2, so 3 is not a divisor of 4775)
...
4775 / 68 = 70.220588235294 (the remainder is 15, so 68 is not a divisor of 4775)
4775 / 69 = 69.202898550725 (the remainder is 14, so 69 is not a divisor of 4775)