What are the divisors of 2984?

1, 2, 4, 8, 373, 746, 1492, 2984

There is a total of 8 positive divisors.
The sum of these divisors is 5610.
The arithmetic mean is 701.25.

6 even divisors

2, 4, 8, 746, 1492, 2984

2 odd divisors

1, 373

How to compute the divisors of 2984?

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 2984 by each of the numbers from 1 to 2984 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)

2984 / 1 = 2984 (the remainder is 0, so 1 is a divisor of 2984)
2984 / 2 = 1492 (the remainder is 0, so 2 is a divisor of 2984)
2984 / 3 = 994.66666666667 (the remainder is 2, so 3 is not a divisor of 2984)
...
2984 / 2983 = 1.0003352329869 (the remainder is 1, so 2983 is not a divisor of 2984)
2984 / 2984 = 1 (the remainder is 0, so 2984 is a divisor of 2984)

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 2984 (i.e. 54.626001134991). 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 $\frac{N}{d} = D$ )

2984 / 1 = 2984 (the remainder is 0, so 1 and 2984 are divisors of 2984)
2984 / 2 = 1492 (the remainder is 0, so 2 and 1492 are divisors of 2984)
2984 / 3 = 994.66666666667 (the remainder is 2, so 3 is not a divisor of 2984)
...
2984 / 53 = 56.301886792453 (the remainder is 16, so 53 is not a divisor of 2984)
2984 / 54 = 55.259259259259 (the remainder is 14, so 54 is not a divisor of 2984)