What are the divisors of 4721?

1, 4721

There is a total of 2 positive divisors.
The sum of these divisors is 4722.
The arithmetic mean is 2361.

2 odd divisors

1, 4721

How to compute the divisors of 4721?

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 4721 by each of the numbers from 1 to 4721 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)

4721 / 1 = 4721 (the remainder is 0, so 1 is a divisor of 4721)
4721 / 2 = 2360.5 (the remainder is 1, so 2 is not a divisor of 4721)
4721 / 3 = 1573.6666666667 (the remainder is 2, so 3 is not a divisor of 4721)
...
4721 / 4720 = 1.0002118644068 (the remainder is 1, so 4720 is not a divisor of 4721)
4721 / 4721 = 1 (the remainder is 0, so 4721 is a divisor of 4721)

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 4721 (i.e. 68.709533545208). 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 $\frac{N}{d} = D$ )

4721 / 1 = 4721 (the remainder is 0, so 1 and 4721 are divisors of 4721)
4721 / 2 = 2360.5 (the remainder is 1, so 2 is not a divisor of 4721)
4721 / 3 = 1573.6666666667 (the remainder is 2, so 3 is not a divisor of 4721)
...
4721 / 67 = 70.462686567164 (the remainder is 31, so 67 is not a divisor of 4721)
4721 / 68 = 69.426470588235 (the remainder is 29, so 68 is not a divisor of 4721)