What are the divisors of 6148?

1, 2, 4, 29, 53, 58, 106, 116, 212, 1537, 3074, 6148

There is a total of 12 positive divisors.
The sum of these divisors is 11340.
The arithmetic mean is 945.

8 even divisors

2, 4, 58, 106, 116, 212, 3074, 6148

4 odd divisors

1, 29, 53, 1537

How to compute the divisors of 6148?

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 6148 by each of the numbers from 1 to 6148 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)

6148 / 1 = 6148 (the remainder is 0, so 1 is a divisor of 6148)
6148 / 2 = 3074 (the remainder is 0, so 2 is a divisor of 6148)
6148 / 3 = 2049.3333333333 (the remainder is 1, so 3 is not a divisor of 6148)
...
6148 / 6147 = 1.0001626809826 (the remainder is 1, so 6147 is not a divisor of 6148)
6148 / 6148 = 1 (the remainder is 0, so 6148 is a divisor of 6148)

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 6148 (i.e. 78.409183135651). 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 $\frac{N}{d} = D$ )

6148 / 1 = 6148 (the remainder is 0, so 1 and 6148 are divisors of 6148)
6148 / 2 = 3074 (the remainder is 0, so 2 and 3074 are divisors of 6148)
6148 / 3 = 2049.3333333333 (the remainder is 1, so 3 is not a divisor of 6148)
...
6148 / 77 = 79.844155844156 (the remainder is 65, so 77 is not a divisor of 6148)
6148 / 78 = 78.820512820513 (the remainder is 64, so 78 is not a divisor of 6148)