What are the divisors of 2767?

1, 2767

There is a total of 2 positive divisors.
The sum of these divisors is 2768.
The arithmetic mean is 1384.

2 odd divisors

1, 2767

How to compute the divisors of 2767?

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 2767 by each of the numbers from 1 to 2767 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)

2767 / 1 = 2767 (the remainder is 0, so 1 is a divisor of 2767)
2767 / 2 = 1383.5 (the remainder is 1, so 2 is not a divisor of 2767)
2767 / 3 = 922.33333333333 (the remainder is 1, so 3 is not a divisor of 2767)
...
2767 / 2766 = 1.0003615328995 (the remainder is 1, so 2766 is not a divisor of 2767)
2767 / 2767 = 1 (the remainder is 0, so 2767 is a divisor of 2767)

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 2767 (i.e. 52.60228131935). 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 $\frac{N}{d} = D$ )

2767 / 1 = 2767 (the remainder is 0, so 1 and 2767 are divisors of 2767)
2767 / 2 = 1383.5 (the remainder is 1, so 2 is not a divisor of 2767)
2767 / 3 = 922.33333333333 (the remainder is 1, so 3 is not a divisor of 2767)
...
2767 / 51 = 54.254901960784 (the remainder is 13, so 51 is not a divisor of 2767)
2767 / 52 = 53.211538461538 (the remainder is 11, so 52 is not a divisor of 2767)