What are the divisors of 2933?

1, 7, 419, 2933

There is a total of 4 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 840.

4 odd divisors

1, 7, 419, 2933

How to compute the divisors of 2933?

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 2933 by each of the numbers from 1 to 2933 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)

2933 / 1 = 2933 (the remainder is 0, so 1 is a divisor of 2933)
2933 / 2 = 1466.5 (the remainder is 1, so 2 is not a divisor of 2933)
2933 / 3 = 977.66666666667 (the remainder is 2, so 3 is not a divisor of 2933)
...
2933 / 2932 = 1.0003410641201 (the remainder is 1, so 2932 is not a divisor of 2933)
2933 / 2933 = 1 (the remainder is 0, so 2933 is a divisor of 2933)

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 2933 (i.e. 54.157178656204). 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 $\frac{N}{d} = D$ )

2933 / 1 = 2933 (the remainder is 0, so 1 and 2933 are divisors of 2933)
2933 / 2 = 1466.5 (the remainder is 1, so 2 is not a divisor of 2933)
2933 / 3 = 977.66666666667 (the remainder is 2, so 3 is not a divisor of 2933)
...
2933 / 53 = 55.339622641509 (the remainder is 18, so 53 is not a divisor of 2933)
2933 / 54 = 54.314814814815 (the remainder is 17, so 54 is not a divisor of 2933)