What are the divisors of 4739?

1, 7, 677, 4739

There is a total of 4 positive divisors.
The sum of these divisors is 5424.
The arithmetic mean is 1356.

4 odd divisors

1, 7, 677, 4739

How to compute the divisors of 4739?

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 4739 by each of the numbers from 1 to 4739 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)

4739 / 1 = 4739 (the remainder is 0, so 1 is a divisor of 4739)
4739 / 2 = 2369.5 (the remainder is 1, so 2 is not a divisor of 4739)
4739 / 3 = 1579.6666666667 (the remainder is 2, so 3 is not a divisor of 4739)
...
4739 / 4738 = 1.0002110595188 (the remainder is 1, so 4738 is not a divisor of 4739)
4739 / 4739 = 1 (the remainder is 0, so 4739 is a divisor of 4739)

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 4739 (i.e. 68.840395117983). 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 $\frac{N}{d} = D$ )

4739 / 1 = 4739 (the remainder is 0, so 1 and 4739 are divisors of 4739)
4739 / 2 = 2369.5 (the remainder is 1, so 2 is not a divisor of 4739)
4739 / 3 = 1579.6666666667 (the remainder is 2, so 3 is not a divisor of 4739)
...
4739 / 67 = 70.731343283582 (the remainder is 49, so 67 is not a divisor of 4739)
4739 / 68 = 69.691176470588 (the remainder is 47, so 68 is not a divisor of 4739)