Enter a number to check if it's square-free, or input a range to generate all square-free numbers within it.
Square-Free Number Check or Generate
Result
Result
What Is a Square-Free Number?
A square-free number is a positive integer that does not include any square factors other than 1. In other words, in the prime factorization of a square-free number, no prime number is raised to a power greater than 1 (i.e., no factor of the form \( p^2 \)).
Examples:
6 (\(2 \times 3\)) and 10 (\(2 \times 5\)) are square-free numbers.
12 (\(2^2 \times 3\)) is not square-free because it contains \( 2^2 \) as a factor.
How to Determine If a Number Is Square-Free
Prime Factorization: Break the number down into its prime factors.
Check for Square Factors: Identify if any prime factor appears with an exponent of 2 or more (e.g., \( p^2 \)).
Result: If a square factor exists, the number is not square-free. If no square factors are present, the number is square-free.
Examples
Example 1: Is 18 a Square-Free Number?
Solution:
Prime factorization: \( 18 = 2 \times 3^2 \).
Result: Since \( 3^2 \) is a square factor, 18 is not square-free.