What are the divisors of 2930?

1, 2, 5, 10, 293, 586, 1465, 2930

There is a total of 8 positive divisors.
The sum of these divisors is 5292.
The arithmetic mean is 661.5.

4 even divisors

2, 10, 586, 2930

4 odd divisors

1, 5, 293, 1465

How to compute the divisors of 2930?

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 2930 by each of the numbers from 1 to 2930 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)

2930 / 1 = 2930 (the remainder is 0, so 1 is a divisor of 2930)
2930 / 2 = 1465 (the remainder is 0, so 2 is a divisor of 2930)
2930 / 3 = 976.66666666667 (the remainder is 2, so 3 is not a divisor of 2930)
...
2930 / 2929 = 1.0003414134517 (the remainder is 1, so 2929 is not a divisor of 2930)
2930 / 2930 = 1 (the remainder is 0, so 2930 is a divisor of 2930)

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 2930 (i.e. 54.129474410897). 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 $\frac{N}{d} = D$ )

2930 / 1 = 2930 (the remainder is 0, so 1 and 2930 are divisors of 2930)
2930 / 2 = 1465 (the remainder is 0, so 2 and 1465 are divisors of 2930)
2930 / 3 = 976.66666666667 (the remainder is 2, so 3 is not a divisor of 2930)
...
2930 / 53 = 55.283018867925 (the remainder is 15, so 53 is not a divisor of 2930)
2930 / 54 = 54.259259259259 (the remainder is 14, so 54 is not a divisor of 2930)