What are the divisors of 4976?

1, 2, 4, 8, 16, 311, 622, 1244, 2488, 4976

There is a total of 10 positive divisors.
The sum of these divisors is 9672.
The arithmetic mean is 967.2.

8 even divisors

2, 4, 8, 16, 622, 1244, 2488, 4976

2 odd divisors

1, 311

How to compute the divisors of 4976?

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 4976 by each of the numbers from 1 to 4976 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)

4976 / 1 = 4976 (the remainder is 0, so 1 is a divisor of 4976)
4976 / 2 = 2488 (the remainder is 0, so 2 is a divisor of 4976)
4976 / 3 = 1658.6666666667 (the remainder is 2, so 3 is not a divisor of 4976)
...
4976 / 4975 = 1.0002010050251 (the remainder is 1, so 4975 is not a divisor of 4976)
4976 / 4976 = 1 (the remainder is 0, so 4976 is a divisor of 4976)

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 4976 (i.e. 70.540768354194). 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 $\frac{N}{d} = D$ )

4976 / 1 = 4976 (the remainder is 0, so 1 and 4976 are divisors of 4976)
4976 / 2 = 2488 (the remainder is 0, so 2 and 2488 are divisors of 4976)
4976 / 3 = 1658.6666666667 (the remainder is 2, so 3 is not a divisor of 4976)
...
4976 / 69 = 72.115942028986 (the remainder is 8, so 69 is not a divisor of 4976)
4976 / 70 = 71.085714285714 (the remainder is 6, so 70 is not a divisor of 4976)