What are the divisors of 2654?

1, 2, 1327, 2654

There is a total of 4 positive divisors.
The sum of these divisors is 3984.
The arithmetic mean is 996.

2 even divisors

2, 2654

2 odd divisors

1, 1327

How to compute the divisors of 2654?

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 2654 by each of the numbers from 1 to 2654 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)

2654 / 1 = 2654 (the remainder is 0, so 1 is a divisor of 2654)
2654 / 2 = 1327 (the remainder is 0, so 2 is a divisor of 2654)
2654 / 3 = 884.66666666667 (the remainder is 2, so 3 is not a divisor of 2654)
...
2654 / 2653 = 1.0003769317753 (the remainder is 1, so 2653 is not a divisor of 2654)
2654 / 2654 = 1 (the remainder is 0, so 2654 is a divisor of 2654)

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 2654 (i.e. 51.516987489565). 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 $\frac{N}{d} = D$ )

2654 / 1 = 2654 (the remainder is 0, so 1 and 2654 are divisors of 2654)
2654 / 2 = 1327 (the remainder is 0, so 2 and 1327 are divisors of 2654)
2654 / 3 = 884.66666666667 (the remainder is 2, so 3 is not a divisor of 2654)
...
2654 / 50 = 53.08 (the remainder is 4, so 50 is not a divisor of 2654)
2654 / 51 = 52.039215686275 (the remainder is 2, so 51 is not a divisor of 2654)