What are the divisors of 4897?

1, 59, 83, 4897

There is a total of 4 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 1260.

4 odd divisors

1, 59, 83, 4897

How to compute the divisors of 4897?

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 4897 by each of the numbers from 1 to 4897 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)

4897 / 1 = 4897 (the remainder is 0, so 1 is a divisor of 4897)
4897 / 2 = 2448.5 (the remainder is 1, so 2 is not a divisor of 4897)
4897 / 3 = 1632.3333333333 (the remainder is 1, so 3 is not a divisor of 4897)
...
4897 / 4896 = 1.000204248366 (the remainder is 1, so 4896 is not a divisor of 4897)
4897 / 4897 = 1 (the remainder is 0, so 4897 is a divisor of 4897)

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 4897 (i.e. 69.978568147684). 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 $\frac{N}{d} = D$ )

4897 / 1 = 4897 (the remainder is 0, so 1 and 4897 are divisors of 4897)
4897 / 2 = 2448.5 (the remainder is 1, so 2 is not a divisor of 4897)
4897 / 3 = 1632.3333333333 (the remainder is 1, so 3 is not a divisor of 4897)
...
4897 / 68 = 72.014705882353 (the remainder is 1, so 68 is not a divisor of 4897)
4897 / 69 = 70.971014492754 (the remainder is 67, so 69 is not a divisor of 4897)