What are the divisors of 4772?

1, 2, 4, 1193, 2386, 4772

There is a total of 6 positive divisors.
The sum of these divisors is 8358.
The arithmetic mean is 1393.

4 even divisors

2, 4, 2386, 4772

2 odd divisors

1, 1193

How to compute the divisors of 4772?

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 4772 by each of the numbers from 1 to 4772 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)

4772 / 1 = 4772 (the remainder is 0, so 1 is a divisor of 4772)
4772 / 2 = 2386 (the remainder is 0, so 2 is a divisor of 4772)
4772 / 3 = 1590.6666666667 (the remainder is 2, so 3 is not a divisor of 4772)
...
4772 / 4771 = 1.0002095996646 (the remainder is 1, so 4771 is not a divisor of 4772)
4772 / 4772 = 1 (the remainder is 0, so 4772 is a divisor of 4772)

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 4772 (i.e. 69.079664156682). 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 $\frac{N}{d} = D$ )

4772 / 1 = 4772 (the remainder is 0, so 1 and 4772 are divisors of 4772)
4772 / 2 = 2386 (the remainder is 0, so 2 and 2386 are divisors of 4772)
4772 / 3 = 1590.6666666667 (the remainder is 2, so 3 is not a divisor of 4772)
...
4772 / 68 = 70.176470588235 (the remainder is 12, so 68 is not a divisor of 4772)
4772 / 69 = 69.159420289855 (the remainder is 11, so 69 is not a divisor of 4772)