What are the divisors of 2653?

1, 7, 379, 2653

There is a total of 4 positive divisors.
The sum of these divisors is 3040.
The arithmetic mean is 760.

4 odd divisors

1, 7, 379, 2653

How to compute the divisors of 2653?

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 2653 by each of the numbers from 1 to 2653 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)

2653 / 1 = 2653 (the remainder is 0, so 1 is a divisor of 2653)
2653 / 2 = 1326.5 (the remainder is 1, so 2 is not a divisor of 2653)
2653 / 3 = 884.33333333333 (the remainder is 1, so 3 is not a divisor of 2653)
...
2653 / 2652 = 1.0003770739065 (the remainder is 1, so 2652 is not a divisor of 2653)
2653 / 2653 = 1 (the remainder is 0, so 2653 is a divisor of 2653)

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 2653 (i.e. 51.507281038704). 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 $\frac{N}{d} = D$ )

2653 / 1 = 2653 (the remainder is 0, so 1 and 2653 are divisors of 2653)
2653 / 2 = 1326.5 (the remainder is 1, so 2 is not a divisor of 2653)
2653 / 3 = 884.33333333333 (the remainder is 1, so 3 is not a divisor of 2653)
...
2653 / 50 = 53.06 (the remainder is 3, so 50 is not a divisor of 2653)
2653 / 51 = 52.019607843137 (the remainder is 1, so 51 is not a divisor of 2653)