What are the divisors of 6154?

1, 2, 17, 34, 181, 362, 3077, 6154

There is a total of 8 positive divisors.
The sum of these divisors is 9828.
The arithmetic mean is 1228.5.

4 even divisors

2, 34, 362, 6154

4 odd divisors

1, 17, 181, 3077

How to compute the divisors of 6154?

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 6154 by each of the numbers from 1 to 6154 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)

6154 / 1 = 6154 (the remainder is 0, so 1 is a divisor of 6154)
6154 / 2 = 3077 (the remainder is 0, so 2 is a divisor of 6154)
6154 / 3 = 2051.3333333333 (the remainder is 1, so 3 is not a divisor of 6154)
...
6154 / 6153 = 1.0001625223468 (the remainder is 1, so 6153 is not a divisor of 6154)
6154 / 6154 = 1 (the remainder is 0, so 6154 is a divisor of 6154)

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 6154 (i.e. 78.447434629821). 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 $\frac{N}{d} = D$ )

6154 / 1 = 6154 (the remainder is 0, so 1 and 6154 are divisors of 6154)
6154 / 2 = 3077 (the remainder is 0, so 2 and 3077 are divisors of 6154)
6154 / 3 = 2051.3333333333 (the remainder is 1, so 3 is not a divisor of 6154)
...
6154 / 77 = 79.922077922078 (the remainder is 71, so 77 is not a divisor of 6154)
6154 / 78 = 78.897435897436 (the remainder is 70, so 78 is not a divisor of 6154)