What are the divisors of 947?

1, 947

There is a total of 2 positive divisors.
The sum of these divisors is 948.
The arithmetic mean is 474.

2 odd divisors

1, 947

How to compute the divisors of 947?

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 947 by each of the numbers from 1 to 947 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)

947 / 1 = 947 (the remainder is 0, so 1 is a divisor of 947)
947 / 2 = 473.5 (the remainder is 1, so 2 is not a divisor of 947)
947 / 3 = 315.66666666667 (the remainder is 2, so 3 is not a divisor of 947)
...
947 / 946 = 1.0010570824524 (the remainder is 1, so 946 is not a divisor of 947)
947 / 947 = 1 (the remainder is 0, so 947 is a divisor of 947)

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 947 (i.e. 30.773365106858). 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 $\frac{N}{d} = D$ )

947 / 1 = 947 (the remainder is 0, so 1 and 947 are divisors of 947)
947 / 2 = 473.5 (the remainder is 1, so 2 is not a divisor of 947)
947 / 3 = 315.66666666667 (the remainder is 2, so 3 is not a divisor of 947)
...
947 / 29 = 32.655172413793 (the remainder is 19, so 29 is not a divisor of 947)
947 / 30 = 31.566666666667 (the remainder is 17, so 30 is not a divisor of 947)