What are the divisors of 2921?

1, 23, 127, 2921

There is a total of 4 positive divisors.
The sum of these divisors is 3072.
The arithmetic mean is 768.

4 odd divisors

1, 23, 127, 2921

How to compute the divisors of 2921?

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 2921 by each of the numbers from 1 to 2921 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)

2921 / 1 = 2921 (the remainder is 0, so 1 is a divisor of 2921)
2921 / 2 = 1460.5 (the remainder is 1, so 2 is not a divisor of 2921)
2921 / 3 = 973.66666666667 (the remainder is 2, so 3 is not a divisor of 2921)
...
2921 / 2920 = 1.0003424657534 (the remainder is 1, so 2920 is not a divisor of 2921)
2921 / 2921 = 1 (the remainder is 0, so 2921 is a divisor of 2921)

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 2921 (i.e. 54.046276467487). 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 $\frac{N}{d} = D$ )

2921 / 1 = 2921 (the remainder is 0, so 1 and 2921 are divisors of 2921)
2921 / 2 = 1460.5 (the remainder is 1, so 2 is not a divisor of 2921)
2921 / 3 = 973.66666666667 (the remainder is 2, so 3 is not a divisor of 2921)
...
2921 / 53 = 55.11320754717 (the remainder is 6, so 53 is not a divisor of 2921)
2921 / 54 = 54.092592592593 (the remainder is 5, so 54 is not a divisor of 2921)