What are the divisors of 2961?

1, 3, 7, 9, 21, 47, 63, 141, 329, 423, 987, 2961

There is a total of 12 positive divisors.
The sum of these divisors is 4992.
The arithmetic mean is 416.

12 odd divisors

1, 3, 7, 9, 21, 47, 63, 141, 329, 423, 987, 2961

How to compute the divisors of 2961?

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 2961 by each of the numbers from 1 to 2961 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)

2961 / 1 = 2961 (the remainder is 0, so 1 is a divisor of 2961)
2961 / 2 = 1480.5 (the remainder is 1, so 2 is not a divisor of 2961)
2961 / 3 = 987 (the remainder is 0, so 3 is a divisor of 2961)
...
2961 / 2960 = 1.0003378378378 (the remainder is 1, so 2960 is not a divisor of 2961)
2961 / 2961 = 1 (the remainder is 0, so 2961 is a divisor of 2961)

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 2961 (i.e. 54.415071441651). 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 $\frac{N}{d} = D$ )

2961 / 1 = 2961 (the remainder is 0, so 1 and 2961 are divisors of 2961)
2961 / 2 = 1480.5 (the remainder is 1, so 2 is not a divisor of 2961)
2961 / 3 = 987 (the remainder is 0, so 3 and 987 are divisors of 2961)
...
2961 / 53 = 55.867924528302 (the remainder is 46, so 53 is not a divisor of 2961)
2961 / 54 = 54.833333333333 (the remainder is 45, so 54 is not a divisor of 2961)