What are the divisors of 2936?

1, 2, 4, 8, 367, 734, 1468, 2936

There is a total of 8 positive divisors.
The sum of these divisors is 5520.
The arithmetic mean is 690.

6 even divisors

2, 4, 8, 734, 1468, 2936

2 odd divisors

1, 367

How to compute the divisors of 2936?

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 2936 by each of the numbers from 1 to 2936 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)

2936 / 1 = 2936 (the remainder is 0, so 1 is a divisor of 2936)
2936 / 2 = 1468 (the remainder is 0, so 2 is a divisor of 2936)
2936 / 3 = 978.66666666667 (the remainder is 2, so 3 is not a divisor of 2936)
...
2936 / 2935 = 1.0003407155026 (the remainder is 1, so 2935 is not a divisor of 2936)
2936 / 2936 = 1 (the remainder is 0, so 2936 is a divisor of 2936)

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 2936 (i.e. 54.184868736576). 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 $\frac{N}{d} = D$ )

2936 / 1 = 2936 (the remainder is 0, so 1 and 2936 are divisors of 2936)
2936 / 2 = 1468 (the remainder is 0, so 2 and 1468 are divisors of 2936)
2936 / 3 = 978.66666666667 (the remainder is 2, so 3 is not a divisor of 2936)
...
2936 / 53 = 55.396226415094 (the remainder is 21, so 53 is not a divisor of 2936)
2936 / 54 = 54.37037037037 (the remainder is 20, so 54 is not a divisor of 2936)