What are the divisors of 662?

1, 2, 331, 662

There is a total of 4 positive divisors.
The sum of these divisors is 996.
The arithmetic mean is 249.

2 even divisors

2, 662

2 odd divisors

1, 331

How to compute the divisors of 662?

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 662 by each of the numbers from 1 to 662 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)

662 / 1 = 662 (the remainder is 0, so 1 is a divisor of 662)
662 / 2 = 331 (the remainder is 0, so 2 is a divisor of 662)
662 / 3 = 220.66666666667 (the remainder is 2, so 3 is not a divisor of 662)
...
662 / 661 = 1.0015128593041 (the remainder is 1, so 661 is not a divisor of 662)
662 / 662 = 1 (the remainder is 0, so 662 is a divisor of 662)

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 662 (i.e. 25.729360660537). 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 $\frac{N}{d} = D$ )

662 / 1 = 662 (the remainder is 0, so 1 and 662 are divisors of 662)
662 / 2 = 331 (the remainder is 0, so 2 and 331 are divisors of 662)
662 / 3 = 220.66666666667 (the remainder is 2, so 3 is not a divisor of 662)
...
662 / 24 = 27.583333333333 (the remainder is 14, so 24 is not a divisor of 662)
662 / 25 = 26.48 (the remainder is 12, so 25 is not a divisor of 662)