What are the divisors of 661?

1, 661

There is a total of 2 positive divisors.
The sum of these divisors is 662.
The arithmetic mean is 331.

2 odd divisors

1, 661

How to compute the divisors of 661?

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 661 by each of the numbers from 1 to 661 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)

661 / 1 = 661 (the remainder is 0, so 1 is a divisor of 661)
661 / 2 = 330.5 (the remainder is 1, so 2 is not a divisor of 661)
661 / 3 = 220.33333333333 (the remainder is 1, so 3 is not a divisor of 661)
...
661 / 660 = 1.0015151515152 (the remainder is 1, so 660 is not a divisor of 661)
661 / 661 = 1 (the remainder is 0, so 661 is a divisor of 661)

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 661 (i.e. 25.709920264365). 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 $\frac{N}{d} = D$ )

661 / 1 = 661 (the remainder is 0, so 1 and 661 are divisors of 661)
661 / 2 = 330.5 (the remainder is 1, so 2 is not a divisor of 661)
661 / 3 = 220.33333333333 (the remainder is 1, so 3 is not a divisor of 661)
...
661 / 24 = 27.541666666667 (the remainder is 13, so 24 is not a divisor of 661)
661 / 25 = 26.44 (the remainder is 11, so 25 is not a divisor of 661)