What are the divisors of 910?

1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910

There is a total of 16 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 126.

8 even divisors

2, 10, 14, 26, 70, 130, 182, 910

8 odd divisors

1, 5, 7, 13, 35, 65, 91, 455

How to compute the divisors of 910?

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 910 by each of the numbers from 1 to 910 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)

910 / 1 = 910 (the remainder is 0, so 1 is a divisor of 910)
910 / 2 = 455 (the remainder is 0, so 2 is a divisor of 910)
910 / 3 = 303.33333333333 (the remainder is 1, so 3 is not a divisor of 910)
...
910 / 909 = 1.001100110011 (the remainder is 1, so 909 is not a divisor of 910)
910 / 910 = 1 (the remainder is 0, so 910 is a divisor of 910)

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 910 (i.e. 30.166206257997). 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 $\frac{N}{d} = D$ )

910 / 1 = 910 (the remainder is 0, so 1 and 910 are divisors of 910)
910 / 2 = 455 (the remainder is 0, so 2 and 455 are divisors of 910)
910 / 3 = 303.33333333333 (the remainder is 1, so 3 is not a divisor of 910)
...
910 / 29 = 31.379310344828 (the remainder is 11, so 29 is not a divisor of 910)
910 / 30 = 30.333333333333 (the remainder is 10, so 30 is not a divisor of 910)