What are the divisors of 970?

1, 2, 5, 10, 97, 194, 485, 970

There is a total of 8 positive divisors.
The sum of these divisors is 1764.
The arithmetic mean is 220.5.

4 even divisors

2, 10, 194, 970

4 odd divisors

1, 5, 97, 485

How to compute the divisors of 970?

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 970 by each of the numbers from 1 to 970 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)

970 / 1 = 970 (the remainder is 0, so 1 is a divisor of 970)
970 / 2 = 485 (the remainder is 0, so 2 is a divisor of 970)
970 / 3 = 323.33333333333 (the remainder is 1, so 3 is not a divisor of 970)
...
970 / 969 = 1.0010319917441 (the remainder is 1, so 969 is not a divisor of 970)
970 / 970 = 1 (the remainder is 0, so 970 is a divisor of 970)

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 970 (i.e. 31.144823004795). 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 $\frac{N}{d} = D$ )

970 / 1 = 970 (the remainder is 0, so 1 and 970 are divisors of 970)
970 / 2 = 485 (the remainder is 0, so 2 and 485 are divisors of 970)
970 / 3 = 323.33333333333 (the remainder is 1, so 3 is not a divisor of 970)
...
970 / 30 = 32.333333333333 (the remainder is 10, so 30 is not a divisor of 970)
970 / 31 = 31.290322580645 (the remainder is 9, so 31 is not a divisor of 970)