What are the divisors of 4799?

1, 4799

There is a total of 2 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 2400.

2 odd divisors

1, 4799

How to compute the divisors of 4799?

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 4799 by each of the numbers from 1 to 4799 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)

4799 / 1 = 4799 (the remainder is 0, so 1 is a divisor of 4799)
4799 / 2 = 2399.5 (the remainder is 1, so 2 is not a divisor of 4799)
4799 / 3 = 1599.6666666667 (the remainder is 2, so 3 is not a divisor of 4799)
...
4799 / 4798 = 1.0002084201751 (the remainder is 1, so 4798 is not a divisor of 4799)
4799 / 4799 = 1 (the remainder is 0, so 4799 is a divisor of 4799)

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 4799 (i.e. 69.274815048472). 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 $\frac{N}{d} = D$ )

4799 / 1 = 4799 (the remainder is 0, so 1 and 4799 are divisors of 4799)
4799 / 2 = 2399.5 (the remainder is 1, so 2 is not a divisor of 4799)
4799 / 3 = 1599.6666666667 (the remainder is 2, so 3 is not a divisor of 4799)
...
4799 / 68 = 70.573529411765 (the remainder is 39, so 68 is not a divisor of 4799)
4799 / 69 = 69.550724637681 (the remainder is 38, so 69 is not a divisor of 4799)