What are the divisors of 6101?

1, 6101

There is a total of 2 positive divisors.
The sum of these divisors is 6102.
The arithmetic mean is 3051.

2 odd divisors

1, 6101

How to compute the divisors of 6101?

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 6101 by each of the numbers from 1 to 6101 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)

6101 / 1 = 6101 (the remainder is 0, so 1 is a divisor of 6101)
6101 / 2 = 3050.5 (the remainder is 1, so 2 is not a divisor of 6101)
6101 / 3 = 2033.6666666667 (the remainder is 2, so 3 is not a divisor of 6101)
...
6101 / 6100 = 1.0001639344262 (the remainder is 1, so 6100 is not a divisor of 6101)
6101 / 6101 = 1 (the remainder is 0, so 6101 is a divisor of 6101)

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 6101 (i.e. 78.108898340714). 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 $\frac{N}{d} = D$ )

6101 / 1 = 6101 (the remainder is 0, so 1 and 6101 are divisors of 6101)
6101 / 2 = 3050.5 (the remainder is 1, so 2 is not a divisor of 6101)
6101 / 3 = 2033.6666666667 (the remainder is 2, so 3 is not a divisor of 6101)
...
6101 / 77 = 79.233766233766 (the remainder is 18, so 77 is not a divisor of 6101)
6101 / 78 = 78.217948717949 (the remainder is 17, so 78 is not a divisor of 6101)