What are the divisors of 2722?

1, 2, 1361, 2722

There is a total of 4 positive divisors.
The sum of these divisors is 4086.
The arithmetic mean is 1021.5.

2 even divisors

2, 2722

2 odd divisors

1, 1361

How to compute the divisors of 2722?

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 2722 by each of the numbers from 1 to 2722 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)

2722 / 1 = 2722 (the remainder is 0, so 1 is a divisor of 2722)
2722 / 2 = 1361 (the remainder is 0, so 2 is a divisor of 2722)
2722 / 3 = 907.33333333333 (the remainder is 1, so 3 is not a divisor of 2722)
...
2722 / 2721 = 1.0003675119441 (the remainder is 1, so 2721 is not a divisor of 2722)
2722 / 2722 = 1 (the remainder is 0, so 2722 is a divisor of 2722)

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 2722 (i.e. 52.172789842982). 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 $\frac{N}{d} = D$ )

2722 / 1 = 2722 (the remainder is 0, so 1 and 2722 are divisors of 2722)
2722 / 2 = 1361 (the remainder is 0, so 2 and 1361 are divisors of 2722)
2722 / 3 = 907.33333333333 (the remainder is 1, so 3 is not a divisor of 2722)
...
2722 / 51 = 53.372549019608 (the remainder is 19, so 51 is not a divisor of 2722)
2722 / 52 = 52.346153846154 (the remainder is 18, so 52 is not a divisor of 2722)