What are the divisors of 890?

1, 2, 5, 10, 89, 178, 445, 890

There is a total of 8 positive divisors.
The sum of these divisors is 1620.
The arithmetic mean is 202.5.

4 even divisors

2, 10, 178, 890

4 odd divisors

1, 5, 89, 445

How to compute the divisors of 890?

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 890 by each of the numbers from 1 to 890 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)

890 / 1 = 890 (the remainder is 0, so 1 is a divisor of 890)
890 / 2 = 445 (the remainder is 0, so 2 is a divisor of 890)
890 / 3 = 296.66666666667 (the remainder is 2, so 3 is not a divisor of 890)
...
890 / 889 = 1.0011248593926 (the remainder is 1, so 889 is not a divisor of 890)
890 / 890 = 1 (the remainder is 0, so 890 is a divisor of 890)

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 890 (i.e. 29.832867780353). 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 $\frac{N}{d} = D$ )

890 / 1 = 890 (the remainder is 0, so 1 and 890 are divisors of 890)
890 / 2 = 445 (the remainder is 0, so 2 and 445 are divisors of 890)
890 / 3 = 296.66666666667 (the remainder is 2, so 3 is not a divisor of 890)
...
890 / 28 = 31.785714285714 (the remainder is 22, so 28 is not a divisor of 890)
890 / 29 = 30.689655172414 (the remainder is 20, so 29 is not a divisor of 890)