What are the divisors of 4898?

1, 2, 31, 62, 79, 158, 2449, 4898

There is a total of 8 positive divisors.
The sum of these divisors is 7680.
The arithmetic mean is 960.

4 even divisors

2, 62, 158, 4898

4 odd divisors

1, 31, 79, 2449

How to compute the divisors of 4898?

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 4898 by each of the numbers from 1 to 4898 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)

4898 / 1 = 4898 (the remainder is 0, so 1 is a divisor of 4898)
4898 / 2 = 2449 (the remainder is 0, so 2 is a divisor of 4898)
4898 / 3 = 1632.6666666667 (the remainder is 2, so 3 is not a divisor of 4898)
...
4898 / 4897 = 1.0002042066571 (the remainder is 1, so 4897 is not a divisor of 4898)
4898 / 4898 = 1 (the remainder is 0, so 4898 is a divisor of 4898)

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 4898 (i.e. 69.985712827691). 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 $\frac{N}{d} = D$ )

4898 / 1 = 4898 (the remainder is 0, so 1 and 4898 are divisors of 4898)
4898 / 2 = 2449 (the remainder is 0, so 2 and 2449 are divisors of 4898)
4898 / 3 = 1632.6666666667 (the remainder is 2, so 3 is not a divisor of 4898)
...
4898 / 68 = 72.029411764706 (the remainder is 2, so 68 is not a divisor of 4898)
4898 / 69 = 70.985507246377 (the remainder is 68, so 69 is not a divisor of 4898)