What are the divisors of 914?

1, 2, 457, 914

There is a total of 4 positive divisors.
The sum of these divisors is 1374.
The arithmetic mean is 343.5.

2 even divisors

2, 914

2 odd divisors

1, 457

How to compute the divisors of 914?

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 914 by each of the numbers from 1 to 914 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)

914 / 1 = 914 (the remainder is 0, so 1 is a divisor of 914)
914 / 2 = 457 (the remainder is 0, so 2 is a divisor of 914)
914 / 3 = 304.66666666667 (the remainder is 2, so 3 is not a divisor of 914)
...
914 / 913 = 1.0010952902519 (the remainder is 1, so 913 is not a divisor of 914)
914 / 914 = 1 (the remainder is 0, so 914 is a divisor of 914)

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 914 (i.e. 30.232432915662). 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 $\frac{N}{d} = D$ )

914 / 1 = 914 (the remainder is 0, so 1 and 914 are divisors of 914)
914 / 2 = 457 (the remainder is 0, so 2 and 457 are divisors of 914)
914 / 3 = 304.66666666667 (the remainder is 2, so 3 is not a divisor of 914)
...
914 / 29 = 31.51724137931 (the remainder is 15, so 29 is not a divisor of 914)
914 / 30 = 30.466666666667 (the remainder is 14, so 30 is not a divisor of 914)