What are the divisors of 4776?

1, 2, 3, 4, 6, 8, 12, 24, 199, 398, 597, 796, 1194, 1592, 2388, 4776

There is a total of 16 positive divisors.
The sum of these divisors is 12000.
The arithmetic mean is 750.

12 even divisors

2, 4, 6, 8, 12, 24, 398, 796, 1194, 1592, 2388, 4776

4 odd divisors

1, 3, 199, 597

How to compute the divisors of 4776?

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 4776 by each of the numbers from 1 to 4776 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)

4776 / 1 = 4776 (the remainder is 0, so 1 is a divisor of 4776)
4776 / 2 = 2388 (the remainder is 0, so 2 is a divisor of 4776)
4776 / 3 = 1592 (the remainder is 0, so 3 is a divisor of 4776)
...
4776 / 4775 = 1.0002094240838 (the remainder is 1, so 4775 is not a divisor of 4776)
4776 / 4776 = 1 (the remainder is 0, so 4776 is a divisor of 4776)

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 4776 (i.e. 69.108610172684). 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 $\frac{N}{d} = D$ )

4776 / 1 = 4776 (the remainder is 0, so 1 and 4776 are divisors of 4776)
4776 / 2 = 2388 (the remainder is 0, so 2 and 2388 are divisors of 4776)
4776 / 3 = 1592 (the remainder is 0, so 3 and 1592 are divisors of 4776)
...
4776 / 68 = 70.235294117647 (the remainder is 16, so 68 is not a divisor of 4776)
4776 / 69 = 69.217391304348 (the remainder is 15, so 69 is not a divisor of 4776)