What are the divisors of 4699?

1, 37, 127, 4699

There is a total of 4 positive divisors.
The sum of these divisors is 4864.
The arithmetic mean is 1216.

4 odd divisors

1, 37, 127, 4699

How to compute the divisors of 4699?

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 4699 by each of the numbers from 1 to 4699 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)

4699 / 1 = 4699 (the remainder is 0, so 1 is a divisor of 4699)
4699 / 2 = 2349.5 (the remainder is 1, so 2 is not a divisor of 4699)
4699 / 3 = 1566.3333333333 (the remainder is 1, so 3 is not a divisor of 4699)
...
4699 / 4698 = 1.0002128565347 (the remainder is 1, so 4698 is not a divisor of 4699)
4699 / 4699 = 1 (the remainder is 0, so 4699 is a divisor of 4699)

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 4699 (i.e. 68.549252366455). 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 $\frac{N}{d} = D$ )

4699 / 1 = 4699 (the remainder is 0, so 1 and 4699 are divisors of 4699)
4699 / 2 = 2349.5 (the remainder is 1, so 2 is not a divisor of 4699)
4699 / 3 = 1566.3333333333 (the remainder is 1, so 3 is not a divisor of 4699)
...
4699 / 67 = 70.134328358209 (the remainder is 9, so 67 is not a divisor of 4699)
4699 / 68 = 69.102941176471 (the remainder is 7, so 68 is not a divisor of 4699)