What are the divisors of 3970?

1, 2, 5, 10, 397, 794, 1985, 3970

There is a total of 8 positive divisors.
The sum of these divisors is 7164.
The arithmetic mean is 895.5.

4 even divisors

2, 10, 794, 3970

4 odd divisors

1, 5, 397, 1985

How to compute the divisors of 3970?

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 3970 by each of the numbers from 1 to 3970 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)

3970 / 1 = 3970 (the remainder is 0, so 1 is a divisor of 3970)
3970 / 2 = 1985 (the remainder is 0, so 2 is a divisor of 3970)
3970 / 3 = 1323.3333333333 (the remainder is 1, so 3 is not a divisor of 3970)
...
3970 / 3969 = 1.0002519526329 (the remainder is 1, so 3969 is not a divisor of 3970)
3970 / 3970 = 1 (the remainder is 0, so 3970 is a divisor of 3970)

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 3970 (i.e. 63.007936008093). 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 $\frac{N}{d} = D$ )

3970 / 1 = 3970 (the remainder is 0, so 1 and 3970 are divisors of 3970)
3970 / 2 = 1985 (the remainder is 0, so 2 and 1985 are divisors of 3970)
3970 / 3 = 1323.3333333333 (the remainder is 1, so 3 is not a divisor of 3970)
...
3970 / 62 = 64.032258064516 (the remainder is 2, so 62 is not a divisor of 3970)
3970 / 63 = 63.015873015873 (the remainder is 1, so 63 is not a divisor of 3970)