What are the divisors of 2996?

1, 2, 4, 7, 14, 28, 107, 214, 428, 749, 1498, 2996

There is a total of 12 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 504.

8 even divisors

2, 4, 14, 28, 214, 428, 1498, 2996

4 odd divisors

1, 7, 107, 749

How to compute the divisors of 2996?

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 2996 by each of the numbers from 1 to 2996 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)

2996 / 1 = 2996 (the remainder is 0, so 1 is a divisor of 2996)
2996 / 2 = 1498 (the remainder is 0, so 2 is a divisor of 2996)
2996 / 3 = 998.66666666667 (the remainder is 2, so 3 is not a divisor of 2996)
...
2996 / 2995 = 1.0003338898164 (the remainder is 1, so 2995 is not a divisor of 2996)
2996 / 2996 = 1 (the remainder is 0, so 2996 is a divisor of 2996)

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 2996 (i.e. 54.735728733616). 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 $\frac{N}{d} = D$ )

2996 / 1 = 2996 (the remainder is 0, so 1 and 2996 are divisors of 2996)
2996 / 2 = 1498 (the remainder is 0, so 2 and 1498 are divisors of 2996)
2996 / 3 = 998.66666666667 (the remainder is 2, so 3 is not a divisor of 2996)
...
2996 / 53 = 56.528301886792 (the remainder is 28, so 53 is not a divisor of 2996)
2996 / 54 = 55.481481481481 (the remainder is 26, so 54 is not a divisor of 2996)