What are the divisors of 4915?

1, 5, 983, 4915

There is a total of 4 positive divisors.
The sum of these divisors is 5904.
The arithmetic mean is 1476.

4 odd divisors

1, 5, 983, 4915

How to compute the divisors of 4915?

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 4915 by each of the numbers from 1 to 4915 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)

4915 / 1 = 4915 (the remainder is 0, so 1 is a divisor of 4915)
4915 / 2 = 2457.5 (the remainder is 1, so 2 is not a divisor of 4915)
4915 / 3 = 1638.3333333333 (the remainder is 1, so 3 is not a divisor of 4915)
...
4915 / 4914 = 1.0002035002035 (the remainder is 1, so 4914 is not a divisor of 4915)
4915 / 4915 = 1 (the remainder is 0, so 4915 is a divisor of 4915)

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 4915 (i.e. 70.107060985324). 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 $\frac{N}{d} = D$ )

4915 / 1 = 4915 (the remainder is 0, so 1 and 4915 are divisors of 4915)
4915 / 2 = 2457.5 (the remainder is 1, so 2 is not a divisor of 4915)
4915 / 3 = 1638.3333333333 (the remainder is 1, so 3 is not a divisor of 4915)
...
4915 / 69 = 71.231884057971 (the remainder is 16, so 69 is not a divisor of 4915)
4915 / 70 = 70.214285714286 (the remainder is 15, so 70 is not a divisor of 4915)