What are the divisors of 4802?

1, 2, 7, 14, 49, 98, 343, 686, 2401, 4802

There is a total of 10 positive divisors.
The sum of these divisors is 8403.
The arithmetic mean is 840.3.

5 even divisors

2, 14, 98, 686, 4802

5 odd divisors

1, 7, 49, 343, 2401

How to compute the divisors of 4802?

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 4802 by each of the numbers from 1 to 4802 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)

4802 / 1 = 4802 (the remainder is 0, so 1 is a divisor of 4802)
4802 / 2 = 2401 (the remainder is 0, so 2 is a divisor of 4802)
4802 / 3 = 1600.6666666667 (the remainder is 2, so 3 is not a divisor of 4802)
...
4802 / 4801 = 1.0002082899396 (the remainder is 1, so 4801 is not a divisor of 4802)
4802 / 4802 = 1 (the remainder is 0, so 4802 is a divisor of 4802)

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 4802 (i.e. 69.296464556282). 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 $\frac{N}{d} = D$ )

4802 / 1 = 4802 (the remainder is 0, so 1 and 4802 are divisors of 4802)
4802 / 2 = 2401 (the remainder is 0, so 2 and 2401 are divisors of 4802)
4802 / 3 = 1600.6666666667 (the remainder is 2, so 3 is not a divisor of 4802)
...
4802 / 68 = 70.617647058824 (the remainder is 42, so 68 is not a divisor of 4802)
4802 / 69 = 69.594202898551 (the remainder is 41, so 69 is not a divisor of 4802)