Calculate rad(n), the product of distinct prime factors
Result
Answer
Step-by-Step Derivation
Radical of an Integer Formula
If n = p1^a1 x p2^a2 x ... x pk^ak
rad(n) = p1 x p2 x ... x pk
The radical of an integer removes repeated prime powers and keeps only the distinct prime factors. It is sometimes called the square-free kernel of a number.
⚠The radical function uses positive integers. For n = 1, the empty product gives rad(1) = 1.
What Is rad(n)?
rad(n) is the product of all distinct primes dividing n. It captures which primes occur in n while ignoring how many times each prime occurs.
Distinct Primes
Each prime factor is counted once.
Exponents Ignored
Powers like 2^3 contribute only 2.
Square-Free Kernel
rad(n) is always square-free.
Factor Structure
It summarizes the prime support of n.
Example: For n = 72 = 2^3 x 3^2, the distinct primes are 2 and 3, so rad(72) = 2 x 3 = 6.
Applications of Integer Radical
Prime FactorsSquare-Free KernelABC ConjectureDivisor TheoryNumber Theory
Frequently Asked Questions
What is a radical of an integer calculator?▼
It computes rad(n), the product of the distinct prime factors of n, counting each prime only once.
What is the rad(n) formula?▼
If n = p1^a1 x p2^a2 x ... x pk^ak, then rad(n) = p1 x p2 x ... x pk.
How do I use this rad(n) calculator?▼
Enter a positive integer and calculate. The tool factors n and multiplies each distinct prime factor once.
Is rad(n) the same as prime factorization?▼
No. Prime factorization keeps exponents, while rad(n) ignores exponents and uses each prime factor once.
Where is the radical function used?▼
It is used in number theory, square-free kernels, ABC conjecture discussions, divisor structure, and prime factor analysis.
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