What are the divisors of 2949?

1, 3, 983, 2949

There is a total of 4 positive divisors.
The sum of these divisors is 3936.
The arithmetic mean is 984.

4 odd divisors

1, 3, 983, 2949

How to compute the divisors of 2949?

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 2949 by each of the numbers from 1 to 2949 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)

2949 / 1 = 2949 (the remainder is 0, so 1 is a divisor of 2949)
2949 / 2 = 1474.5 (the remainder is 1, so 2 is not a divisor of 2949)
2949 / 3 = 983 (the remainder is 0, so 3 is a divisor of 2949)
...
2949 / 2948 = 1.0003392130258 (the remainder is 1, so 2948 is not a divisor of 2949)
2949 / 2949 = 1 (the remainder is 0, so 2949 is a divisor of 2949)

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 2949 (i.e. 54.304695929542). 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 $\frac{N}{d} = D$ )

2949 / 1 = 2949 (the remainder is 0, so 1 and 2949 are divisors of 2949)
2949 / 2 = 1474.5 (the remainder is 1, so 2 is not a divisor of 2949)
2949 / 3 = 983 (the remainder is 0, so 3 and 983 are divisors of 2949)
...
2949 / 53 = 55.641509433962 (the remainder is 34, so 53 is not a divisor of 2949)
2949 / 54 = 54.611111111111 (the remainder is 33, so 54 is not a divisor of 2949)