What are the divisors of 2603?

1, 19, 137, 2603

There is a total of 4 positive divisors.
The sum of these divisors is 2760.
The arithmetic mean is 690.

4 odd divisors

1, 19, 137, 2603

How to compute the divisors of 2603?

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 2603 by each of the numbers from 1 to 2603 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)

2603 / 1 = 2603 (the remainder is 0, so 1 is a divisor of 2603)
2603 / 2 = 1301.5 (the remainder is 1, so 2 is not a divisor of 2603)
2603 / 3 = 867.66666666667 (the remainder is 2, so 3 is not a divisor of 2603)
...
2603 / 2602 = 1.000384319754 (the remainder is 1, so 2602 is not a divisor of 2603)
2603 / 2603 = 1 (the remainder is 0, so 2603 is a divisor of 2603)

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 2603 (i.e. 51.019604075296). 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 $\frac{N}{d} = D$ )

2603 / 1 = 2603 (the remainder is 0, so 1 and 2603 are divisors of 2603)
2603 / 2 = 1301.5 (the remainder is 1, so 2 is not a divisor of 2603)
2603 / 3 = 867.66666666667 (the remainder is 2, so 3 is not a divisor of 2603)
...
2603 / 50 = 52.06 (the remainder is 3, so 50 is not a divisor of 2603)
2603 / 51 = 51.039215686275 (the remainder is 2, so 51 is not a divisor of 2603)