What are the divisors of 4997?

1, 19, 263, 4997

There is a total of 4 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 1320.

4 odd divisors

1, 19, 263, 4997

How to compute the divisors of 4997?

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 4997 by each of the numbers from 1 to 4997 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)

4997 / 1 = 4997 (the remainder is 0, so 1 is a divisor of 4997)
4997 / 2 = 2498.5 (the remainder is 1, so 2 is not a divisor of 4997)
4997 / 3 = 1665.6666666667 (the remainder is 2, so 3 is not a divisor of 4997)
...
4997 / 4996 = 1.0002001601281 (the remainder is 1, so 4996 is not a divisor of 4997)
4997 / 4997 = 1 (the remainder is 0, so 4997 is a divisor of 4997)

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 4997 (i.e. 70.689461732284). 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 $\frac{N}{d} = D$ )

4997 / 1 = 4997 (the remainder is 0, so 1 and 4997 are divisors of 4997)
4997 / 2 = 2498.5 (the remainder is 1, so 2 is not a divisor of 4997)
4997 / 3 = 1665.6666666667 (the remainder is 2, so 3 is not a divisor of 4997)
...
4997 / 69 = 72.420289855072 (the remainder is 29, so 69 is not a divisor of 4997)
4997 / 70 = 71.385714285714 (the remainder is 27, so 70 is not a divisor of 4997)