What are the divisors of 1661?

1, 11, 151, 1661

There is a total of 4 positive divisors.
The sum of these divisors is 1824.
The arithmetic mean is 456.

4 odd divisors

1, 11, 151, 1661

How to compute the divisors of 1661?

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 1661 by each of the numbers from 1 to 1661 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)

1661 / 1 = 1661 (the remainder is 0, so 1 is a divisor of 1661)
1661 / 2 = 830.5 (the remainder is 1, so 2 is not a divisor of 1661)
1661 / 3 = 553.66666666667 (the remainder is 2, so 3 is not a divisor of 1661)
...
1661 / 1660 = 1.0006024096386 (the remainder is 1, so 1660 is not a divisor of 1661)
1661 / 1661 = 1 (the remainder is 0, so 1661 is a divisor of 1661)

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 1661 (i.e. 40.75536774463). 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 $\frac{N}{d} = D$ )

1661 / 1 = 1661 (the remainder is 0, so 1 and 1661 are divisors of 1661)
1661 / 2 = 830.5 (the remainder is 1, so 2 is not a divisor of 1661)
1661 / 3 = 553.66666666667 (the remainder is 2, so 3 is not a divisor of 1661)
...
1661 / 39 = 42.589743589744 (the remainder is 23, so 39 is not a divisor of 1661)
1661 / 40 = 41.525 (the remainder is 21, so 40 is not a divisor of 1661)