What are the divisors of 988?

1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494, 988

There is a total of 12 positive divisors.
The sum of these divisors is 1960.
The arithmetic mean is 163.33333333333.

8 even divisors

2, 4, 26, 38, 52, 76, 494, 988

4 odd divisors

1, 13, 19, 247

How to compute the divisors of 988?

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 988 by each of the numbers from 1 to 988 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)

988 / 1 = 988 (the remainder is 0, so 1 is a divisor of 988)
988 / 2 = 494 (the remainder is 0, so 2 is a divisor of 988)
988 / 3 = 329.33333333333 (the remainder is 1, so 3 is not a divisor of 988)
...
988 / 987 = 1.0010131712259 (the remainder is 1, so 987 is not a divisor of 988)
988 / 988 = 1 (the remainder is 0, so 988 is a divisor of 988)

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 988 (i.e. 31.432467291003). 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 $\frac{N}{d} = D$ )

988 / 1 = 988 (the remainder is 0, so 1 and 988 are divisors of 988)
988 / 2 = 494 (the remainder is 0, so 2 and 494 are divisors of 988)
988 / 3 = 329.33333333333 (the remainder is 1, so 3 is not a divisor of 988)
...
988 / 30 = 32.933333333333 (the remainder is 28, so 30 is not a divisor of 988)
988 / 31 = 31.870967741935 (the remainder is 27, so 31 is not a divisor of 988)