What are the divisors of 614?

1, 2, 307, 614

There is a total of 4 positive divisors.
The sum of these divisors is 924.
The arithmetic mean is 231.

2 even divisors

2, 614

2 odd divisors

1, 307

How to compute the divisors of 614?

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 614 by each of the numbers from 1 to 614 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)

614 / 1 = 614 (the remainder is 0, so 1 is a divisor of 614)
614 / 2 = 307 (the remainder is 0, so 2 is a divisor of 614)
614 / 3 = 204.66666666667 (the remainder is 2, so 3 is not a divisor of 614)
...
614 / 613 = 1.0016313213703 (the remainder is 1, so 613 is not a divisor of 614)
614 / 614 = 1 (the remainder is 0, so 614 is a divisor of 614)

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 614 (i.e. 24.779023386728). 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 $\frac{N}{d} = D$ )

614 / 1 = 614 (the remainder is 0, so 1 and 614 are divisors of 614)
614 / 2 = 307 (the remainder is 0, so 2 and 307 are divisors of 614)
614 / 3 = 204.66666666667 (the remainder is 2, so 3 is not a divisor of 614)
...
614 / 23 = 26.695652173913 (the remainder is 16, so 23 is not a divisor of 614)
614 / 24 = 25.583333333333 (the remainder is 14, so 24 is not a divisor of 614)