What are the divisors of 4984?

1, 2, 4, 7, 8, 14, 28, 56, 89, 178, 356, 623, 712, 1246, 2492, 4984

There is a total of 16 positive divisors.
The sum of these divisors is 10800.
The arithmetic mean is 675.

12 even divisors

2, 4, 8, 14, 28, 56, 178, 356, 712, 1246, 2492, 4984

4 odd divisors

1, 7, 89, 623

How to compute the divisors of 4984?

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 4984 by each of the numbers from 1 to 4984 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)

4984 / 1 = 4984 (the remainder is 0, so 1 is a divisor of 4984)
4984 / 2 = 2492 (the remainder is 0, so 2 is a divisor of 4984)
4984 / 3 = 1661.3333333333 (the remainder is 1, so 3 is not a divisor of 4984)
...
4984 / 4983 = 1.0002006823199 (the remainder is 1, so 4983 is not a divisor of 4984)
4984 / 4984 = 1 (the remainder is 0, so 4984 is a divisor of 4984)

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 4984 (i.e. 70.597450378891). 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 $\frac{N}{d} = D$ )

4984 / 1 = 4984 (the remainder is 0, so 1 and 4984 are divisors of 4984)
4984 / 2 = 2492 (the remainder is 0, so 2 and 2492 are divisors of 4984)
4984 / 3 = 1661.3333333333 (the remainder is 1, so 3 is not a divisor of 4984)
...
4984 / 69 = 72.231884057971 (the remainder is 16, so 69 is not a divisor of 4984)
4984 / 70 = 71.2 (the remainder is 14, so 70 is not a divisor of 4984)