What are the divisors of 3070?

1, 2, 5, 10, 307, 614, 1535, 3070

There is a total of 8 positive divisors.
The sum of these divisors is 5544.
The arithmetic mean is 693.

4 even divisors

2, 10, 614, 3070

4 odd divisors

1, 5, 307, 1535

How to compute the divisors of 3070?

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 3070 by each of the numbers from 1 to 3070 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)

3070 / 1 = 3070 (the remainder is 0, so 1 is a divisor of 3070)
3070 / 2 = 1535 (the remainder is 0, so 2 is a divisor of 3070)
3070 / 3 = 1023.3333333333 (the remainder is 1, so 3 is not a divisor of 3070)
...
3070 / 3069 = 1.0003258390355 (the remainder is 1, so 3069 is not a divisor of 3070)
3070 / 3070 = 1 (the remainder is 0, so 3070 is a divisor of 3070)

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 3070 (i.e. 55.40758070878). 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 $\frac{N}{d} = D$ )

3070 / 1 = 3070 (the remainder is 0, so 1 and 3070 are divisors of 3070)
3070 / 2 = 1535 (the remainder is 0, so 2 and 1535 are divisors of 3070)
3070 / 3 = 1023.3333333333 (the remainder is 1, so 3 is not a divisor of 3070)
...
3070 / 54 = 56.851851851852 (the remainder is 46, so 54 is not a divisor of 3070)
3070 / 55 = 55.818181818182 (the remainder is 45, so 55 is not a divisor of 3070)