What are the divisors of 2956?

1, 2, 4, 739, 1478, 2956

There is a total of 6 positive divisors.
The sum of these divisors is 5180.
The arithmetic mean is 863.33333333333.

4 even divisors

2, 4, 1478, 2956

2 odd divisors

1, 739

How to compute the divisors of 2956?

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 2956 by each of the numbers from 1 to 2956 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)

2956 / 1 = 2956 (the remainder is 0, so 1 is a divisor of 2956)
2956 / 2 = 1478 (the remainder is 0, so 2 is a divisor of 2956)
2956 / 3 = 985.33333333333 (the remainder is 1, so 3 is not a divisor of 2956)
...
2956 / 2955 = 1.0003384094755 (the remainder is 1, so 2955 is not a divisor of 2956)
2956 / 2956 = 1 (the remainder is 0, so 2956 is a divisor of 2956)

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 2956 (i.e. 54.369108876273). 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 $\frac{N}{d} = D$ )

2956 / 1 = 2956 (the remainder is 0, so 1 and 2956 are divisors of 2956)
2956 / 2 = 1478 (the remainder is 0, so 2 and 1478 are divisors of 2956)
2956 / 3 = 985.33333333333 (the remainder is 1, so 3 is not a divisor of 2956)
...
2956 / 53 = 55.77358490566 (the remainder is 41, so 53 is not a divisor of 2956)
2956 / 54 = 54.740740740741 (the remainder is 40, so 54 is not a divisor of 2956)