What are the divisors of 938?

1, 2, 7, 14, 67, 134, 469, 938

There is a total of 8 positive divisors.
The sum of these divisors is 1632.
The arithmetic mean is 204.

4 even divisors

2, 14, 134, 938

4 odd divisors

1, 7, 67, 469

How to compute the divisors of 938?

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 938 by each of the numbers from 1 to 938 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)

938 / 1 = 938 (the remainder is 0, so 1 is a divisor of 938)
938 / 2 = 469 (the remainder is 0, so 2 is a divisor of 938)
938 / 3 = 312.66666666667 (the remainder is 2, so 3 is not a divisor of 938)
...
938 / 937 = 1.0010672358591 (the remainder is 1, so 937 is not a divisor of 938)
938 / 938 = 1 (the remainder is 0, so 938 is a divisor of 938)

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 938 (i.e. 30.626785662227). 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 $\frac{N}{d} = D$ )

938 / 1 = 938 (the remainder is 0, so 1 and 938 are divisors of 938)
938 / 2 = 469 (the remainder is 0, so 2 and 469 are divisors of 938)
938 / 3 = 312.66666666667 (the remainder is 2, so 3 is not a divisor of 938)
...
938 / 29 = 32.344827586207 (the remainder is 10, so 29 is not a divisor of 938)
938 / 30 = 31.266666666667 (the remainder is 8, so 30 is not a divisor of 938)