What are the divisors of 994?

1, 2, 7, 14, 71, 142, 497, 994

There is a total of 8 positive divisors.
The sum of these divisors is 1728.
The arithmetic mean is 216.

4 even divisors

2, 14, 142, 994

4 odd divisors

1, 7, 71, 497

How to compute the divisors of 994?

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 994 by each of the numbers from 1 to 994 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)

994 / 1 = 994 (the remainder is 0, so 1 is a divisor of 994)
994 / 2 = 497 (the remainder is 0, so 2 is a divisor of 994)
994 / 3 = 331.33333333333 (the remainder is 1, so 3 is not a divisor of 994)
...
994 / 993 = 1.0010070493454 (the remainder is 1, so 993 is not a divisor of 994)
994 / 994 = 1 (the remainder is 0, so 994 is a divisor of 994)

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 994 (i.e. 31.527765540869). 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 $\frac{N}{d} = D$ )

994 / 1 = 994 (the remainder is 0, so 1 and 994 are divisors of 994)
994 / 2 = 497 (the remainder is 0, so 2 and 497 are divisors of 994)
994 / 3 = 331.33333333333 (the remainder is 1, so 3 is not a divisor of 994)
...
994 / 30 = 33.133333333333 (the remainder is 4, so 30 is not a divisor of 994)
994 / 31 = 32.064516129032 (the remainder is 2, so 31 is not a divisor of 994)