What are the divisors of 6153?

1, 3, 7, 21, 293, 879, 2051, 6153

There is a total of 8 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 1176.

8 odd divisors

1, 3, 7, 21, 293, 879, 2051, 6153

How to compute the divisors of 6153?

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 6153 by each of the numbers from 1 to 6153 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)

6153 / 1 = 6153 (the remainder is 0, so 1 is a divisor of 6153)
6153 / 2 = 3076.5 (the remainder is 1, so 2 is not a divisor of 6153)
6153 / 3 = 2051 (the remainder is 0, so 3 is a divisor of 6153)
...
6153 / 6152 = 1.0001625487646 (the remainder is 1, so 6152 is not a divisor of 6153)
6153 / 6153 = 1 (the remainder is 0, so 6153 is a divisor of 6153)

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 6153 (i.e. 78.441060676154). 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 $\frac{N}{d} = D$ )

6153 / 1 = 6153 (the remainder is 0, so 1 and 6153 are divisors of 6153)
6153 / 2 = 3076.5 (the remainder is 1, so 2 is not a divisor of 6153)
6153 / 3 = 2051 (the remainder is 0, so 3 and 2051 are divisors of 6153)
...
6153 / 77 = 79.909090909091 (the remainder is 70, so 77 is not a divisor of 6153)
6153 / 78 = 78.884615384615 (the remainder is 69, so 78 is not a divisor of 6153)