What are the divisors of 2947?

1, 7, 421, 2947

There is a total of 4 positive divisors.
The sum of these divisors is 3376.
The arithmetic mean is 844.

4 odd divisors

1, 7, 421, 2947

How to compute the divisors of 2947?

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 2947 by each of the numbers from 1 to 2947 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)

2947 / 1 = 2947 (the remainder is 0, so 1 is a divisor of 2947)
2947 / 2 = 1473.5 (the remainder is 1, so 2 is not a divisor of 2947)
2947 / 3 = 982.33333333333 (the remainder is 1, so 3 is not a divisor of 2947)
...
2947 / 2946 = 1.000339443313 (the remainder is 1, so 2946 is not a divisor of 2947)
2947 / 2947 = 1 (the remainder is 0, so 2947 is a divisor of 2947)

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 2947 (i.e. 54.28627819256). 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 $\frac{N}{d} = D$ )

2947 / 1 = 2947 (the remainder is 0, so 1 and 2947 are divisors of 2947)
2947 / 2 = 1473.5 (the remainder is 1, so 2 is not a divisor of 2947)
2947 / 3 = 982.33333333333 (the remainder is 1, so 3 is not a divisor of 2947)
...
2947 / 53 = 55.603773584906 (the remainder is 32, so 53 is not a divisor of 2947)
2947 / 54 = 54.574074074074 (the remainder is 31, so 54 is not a divisor of 2947)