What are the divisors of 4722?

1, 2, 3, 6, 787, 1574, 2361, 4722

There is a total of 8 positive divisors.
The sum of these divisors is 9456.
The arithmetic mean is 1182.

4 even divisors

2, 6, 1574, 4722

4 odd divisors

1, 3, 787, 2361

How to compute the divisors of 4722?

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 4722 by each of the numbers from 1 to 4722 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)

4722 / 1 = 4722 (the remainder is 0, so 1 is a divisor of 4722)
4722 / 2 = 2361 (the remainder is 0, so 2 is a divisor of 4722)
4722 / 3 = 1574 (the remainder is 0, so 3 is a divisor of 4722)
...
4722 / 4721 = 1.0002118195298 (the remainder is 1, so 4721 is not a divisor of 4722)
4722 / 4722 = 1 (the remainder is 0, so 4722 is a divisor of 4722)

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 4722 (i.e. 68.716810170438). 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 $\frac{N}{d} = D$ )

4722 / 1 = 4722 (the remainder is 0, so 1 and 4722 are divisors of 4722)
4722 / 2 = 2361 (the remainder is 0, so 2 and 2361 are divisors of 4722)
4722 / 3 = 1574 (the remainder is 0, so 3 and 1574 are divisors of 4722)
...
4722 / 67 = 70.477611940299 (the remainder is 32, so 67 is not a divisor of 4722)
4722 / 68 = 69.441176470588 (the remainder is 30, so 68 is not a divisor of 4722)