What are the divisors of 2906?

1, 2, 1453, 2906

There is a total of 4 positive divisors.
The sum of these divisors is 4362.
The arithmetic mean is 1090.5.

2 even divisors

2, 2906

2 odd divisors

1, 1453

How to compute the divisors of 2906?

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 2906 by each of the numbers from 1 to 2906 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)

2906 / 1 = 2906 (the remainder is 0, so 1 is a divisor of 2906)
2906 / 2 = 1453 (the remainder is 0, so 2 is a divisor of 2906)
2906 / 3 = 968.66666666667 (the remainder is 2, so 3 is not a divisor of 2906)
...
2906 / 2905 = 1.0003442340792 (the remainder is 1, so 2905 is not a divisor of 2906)
2906 / 2906 = 1 (the remainder is 0, so 2906 is a divisor of 2906)

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 2906 (i.e. 53.907327887774). 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 $\frac{N}{d} = D$ )

2906 / 1 = 2906 (the remainder is 0, so 1 and 2906 are divisors of 2906)
2906 / 2 = 1453 (the remainder is 0, so 2 and 1453 are divisors of 2906)
2906 / 3 = 968.66666666667 (the remainder is 2, so 3 is not a divisor of 2906)
...
2906 / 52 = 55.884615384615 (the remainder is 46, so 52 is not a divisor of 2906)
2906 / 53 = 54.830188679245 (the remainder is 44, so 53 is not a divisor of 2906)