What are the divisors of 2614?

1, 2, 1307, 2614

There is a total of 4 positive divisors.
The sum of these divisors is 3924.
The arithmetic mean is 981.

2 even divisors

2, 2614

2 odd divisors

1, 1307

How to compute the divisors of 2614?

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 2614 by each of the numbers from 1 to 2614 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)

2614 / 1 = 2614 (the remainder is 0, so 1 is a divisor of 2614)
2614 / 2 = 1307 (the remainder is 0, so 2 is a divisor of 2614)
2614 / 3 = 871.33333333333 (the remainder is 1, so 3 is not a divisor of 2614)
...
2614 / 2613 = 1.0003827018752 (the remainder is 1, so 2613 is not a divisor of 2614)
2614 / 2614 = 1 (the remainder is 0, so 2614 is a divisor of 2614)

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 2614 (i.e. 51.127292124657). 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 $\frac{N}{d} = D$ )

2614 / 1 = 2614 (the remainder is 0, so 1 and 2614 are divisors of 2614)
2614 / 2 = 1307 (the remainder is 0, so 2 and 1307 are divisors of 2614)
2614 / 3 = 871.33333333333 (the remainder is 1, so 3 is not a divisor of 2614)
...
2614 / 50 = 52.28 (the remainder is 14, so 50 is not a divisor of 2614)
2614 / 51 = 51.254901960784 (the remainder is 13, so 51 is not a divisor of 2614)