What are the divisors of 5051?

1, 5051

There is a total of 2 positive divisors.
The sum of these divisors is 5052.
The arithmetic mean is 2526.

2 odd divisors

1, 5051

How to compute the divisors of 5051?

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 5051 by each of the numbers from 1 to 5051 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)

5051 / 1 = 5051 (the remainder is 0, so 1 is a divisor of 5051)
5051 / 2 = 2525.5 (the remainder is 1, so 2 is not a divisor of 5051)
5051 / 3 = 1683.6666666667 (the remainder is 2, so 3 is not a divisor of 5051)
...
5051 / 5050 = 1.000198019802 (the remainder is 1, so 5050 is not a divisor of 5051)
5051 / 5051 = 1 (the remainder is 0, so 5051 is a divisor of 5051)

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 5051 (i.e. 71.070387644926). 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 $\frac{N}{d} = D$ )

5051 / 1 = 5051 (the remainder is 0, so 1 and 5051 are divisors of 5051)
5051 / 2 = 2525.5 (the remainder is 1, so 2 is not a divisor of 5051)
5051 / 3 = 1683.6666666667 (the remainder is 2, so 3 is not a divisor of 5051)
...
5051 / 70 = 72.157142857143 (the remainder is 11, so 70 is not a divisor of 5051)
5051 / 71 = 71.140845070423 (the remainder is 10, so 71 is not a divisor of 5051)