What are the divisors of 6151?

1, 6151

There is a total of 2 positive divisors.
The sum of these divisors is 6152.
The arithmetic mean is 3076.

2 odd divisors

1, 6151

How to compute the divisors of 6151?

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 6151 by each of the numbers from 1 to 6151 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)

6151 / 1 = 6151 (the remainder is 0, so 1 is a divisor of 6151)
6151 / 2 = 3075.5 (the remainder is 1, so 2 is not a divisor of 6151)
6151 / 3 = 2050.3333333333 (the remainder is 1, so 3 is not a divisor of 6151)
...
6151 / 6150 = 1.000162601626 (the remainder is 1, so 6150 is not a divisor of 6151)
6151 / 6151 = 1 (the remainder is 0, so 6151 is a divisor of 6151)

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 6151 (i.e. 78.428311214765). 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 $\frac{N}{d} = D$ )

6151 / 1 = 6151 (the remainder is 0, so 1 and 6151 are divisors of 6151)
6151 / 2 = 3075.5 (the remainder is 1, so 2 is not a divisor of 6151)
6151 / 3 = 2050.3333333333 (the remainder is 1, so 3 is not a divisor of 6151)
...
6151 / 77 = 79.883116883117 (the remainder is 68, so 77 is not a divisor of 6151)
6151 / 78 = 78.858974358974 (the remainder is 67, so 78 is not a divisor of 6151)