Unitary Divisor Calculator

Input an integer to generate its complete list of unitary divisors.

Calculate the Unitary Divisors of an Integer

Result

What Are Unitary Divisors? How to Calculate Them?

A unitary divisor of a number \( b \) is a special type of divisor \( a \), where \( a \) is a divisor of \( b \), and \( a \) is coprime to \( \frac{b}{a} \) (i.e., their greatest common divisor is 1).

To calculate the unitary divisors of an integer \( N \), follow these steps:

Find all divisors: List all divisors of \( N \), including 1 and \( N \) itself.
Check for coprimality: For each divisor \( a \), verify if \( a \) and \( \frac{N}{a} \) are coprime (i.e., \( \text{GCD}(a, \frac{N}{a}) = 1 \)).
List the unitary divisors: If the coprime condition is satisfied, \( a \) is a unitary divisor of \( N \).

Examples

Example 1: Find the unitary divisors of 36

Solution:

1. Find all divisors:

Divisors of 36: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \).

2. Check for coprimality:

\( 1 \) and \( \frac{36}{1} = 36 \): coprime.

\( 4 \) and \( \frac{36}{4} = 9 \): coprime.

3. List the unitary divisors:

Unitary divisors of 36: \( 1, 4, 9, 36 \).

Example 2: Find the unitary divisors of 60

Solution:

1. Find all divisors:

Divisors of 60: \( 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 \).

2. Check for coprimality:

\( 1 \) and \( \frac{60}{1} = 60 \): coprime.

\( 3 \) and \( \frac{60}{3} = 20 \): coprime.

\( 4 \) and \( \frac{60}{4} = 15 \): coprime.

\( 5 \) and \( \frac{60}{5} = 12 \): coprime.