What are the divisors of 2939?

1, 2939

There is a total of 2 positive divisors.
The sum of these divisors is 2940.
The arithmetic mean is 1470.

2 odd divisors

1, 2939

How to compute the divisors of 2939?

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 2939 by each of the numbers from 1 to 2939 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)

2939 / 1 = 2939 (the remainder is 0, so 1 is a divisor of 2939)
2939 / 2 = 1469.5 (the remainder is 1, so 2 is not a divisor of 2939)
2939 / 3 = 979.66666666667 (the remainder is 2, so 3 is not a divisor of 2939)
...
2939 / 2938 = 1.000340367597 (the remainder is 1, so 2938 is not a divisor of 2939)
2939 / 2939 = 1 (the remainder is 0, so 2939 is a divisor of 2939)

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 2939 (i.e. 54.212544673719). 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 $\frac{N}{d} = D$ )

2939 / 1 = 2939 (the remainder is 0, so 1 and 2939 are divisors of 2939)
2939 / 2 = 1469.5 (the remainder is 1, so 2 is not a divisor of 2939)
2939 / 3 = 979.66666666667 (the remainder is 2, so 3 is not a divisor of 2939)
...
2939 / 53 = 55.452830188679 (the remainder is 24, so 53 is not a divisor of 2939)
2939 / 54 = 54.425925925926 (the remainder is 23, so 54 is not a divisor of 2939)