What are the divisors of 4910?

1, 2, 5, 10, 491, 982, 2455, 4910

There is a total of 8 positive divisors.
The sum of these divisors is 8856.
The arithmetic mean is 1107.

4 even divisors

2, 10, 982, 4910

4 odd divisors

1, 5, 491, 2455

How to compute the divisors of 4910?

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 4910 by each of the numbers from 1 to 4910 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)

4910 / 1 = 4910 (the remainder is 0, so 1 is a divisor of 4910)
4910 / 2 = 2455 (the remainder is 0, so 2 is a divisor of 4910)
4910 / 3 = 1636.6666666667 (the remainder is 2, so 3 is not a divisor of 4910)
...
4910 / 4909 = 1.0002037074761 (the remainder is 1, so 4909 is not a divisor of 4910)
4910 / 4910 = 1 (the remainder is 0, so 4910 is a divisor of 4910)

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 4910 (i.e. 70.071392165419). 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 $\frac{N}{d} = D$ )

4910 / 1 = 4910 (the remainder is 0, so 1 and 4910 are divisors of 4910)
4910 / 2 = 2455 (the remainder is 0, so 2 and 2455 are divisors of 4910)
4910 / 3 = 1636.6666666667 (the remainder is 2, so 3 is not a divisor of 4910)
...
4910 / 69 = 71.159420289855 (the remainder is 11, so 69 is not a divisor of 4910)
4910 / 70 = 70.142857142857 (the remainder is 10, so 70 is not a divisor of 4910)