What are the divisors of 2734?

1, 2, 1367, 2734

There is a total of 4 positive divisors.
The sum of these divisors is 4104.
The arithmetic mean is 1026.

2 even divisors

2, 2734

2 odd divisors

1, 1367

How to compute the divisors of 2734?

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 2734 by each of the numbers from 1 to 2734 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)

2734 / 1 = 2734 (the remainder is 0, so 1 is a divisor of 2734)
2734 / 2 = 1367 (the remainder is 0, so 2 is a divisor of 2734)
2734 / 3 = 911.33333333333 (the remainder is 1, so 3 is not a divisor of 2734)
...
2734 / 2733 = 1.0003658982803 (the remainder is 1, so 2733 is not a divisor of 2734)
2734 / 2734 = 1 (the remainder is 0, so 2734 is a divisor of 2734)

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 2734 (i.e. 52.287665849605). 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 $\frac{N}{d} = D$ )

2734 / 1 = 2734 (the remainder is 0, so 1 and 2734 are divisors of 2734)
2734 / 2 = 1367 (the remainder is 0, so 2 and 1367 are divisors of 2734)
2734 / 3 = 911.33333333333 (the remainder is 1, so 3 is not a divisor of 2734)
...
2734 / 51 = 53.607843137255 (the remainder is 31, so 51 is not a divisor of 2734)
2734 / 52 = 52.576923076923 (the remainder is 30, so 52 is not a divisor of 2734)