What are the divisors of 4975?

1, 5, 25, 199, 995, 4975

There is a total of 6 positive divisors.
The sum of these divisors is 6200.
The arithmetic mean is 1033.3333333333.

6 odd divisors

1, 5, 25, 199, 995, 4975

How to compute the divisors of 4975?

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 4975 by each of the numbers from 1 to 4975 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)

4975 / 1 = 4975 (the remainder is 0, so 1 is a divisor of 4975)
4975 / 2 = 2487.5 (the remainder is 1, so 2 is not a divisor of 4975)
4975 / 3 = 1658.3333333333 (the remainder is 1, so 3 is not a divisor of 4975)
...
4975 / 4974 = 1.0002010454363 (the remainder is 1, so 4974 is not a divisor of 4975)
4975 / 4975 = 1 (the remainder is 0, so 4975 is a divisor of 4975)

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 4975 (i.e. 70.533679898329). 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 $\frac{N}{d} = D$ )

4975 / 1 = 4975 (the remainder is 0, so 1 and 4975 are divisors of 4975)
4975 / 2 = 2487.5 (the remainder is 1, so 2 is not a divisor of 4975)
4975 / 3 = 1658.3333333333 (the remainder is 1, so 3 is not a divisor of 4975)
...
4975 / 69 = 72.101449275362 (the remainder is 7, so 69 is not a divisor of 4975)
4975 / 70 = 71.071428571429 (the remainder is 5, so 70 is not a divisor of 4975)