Find the complete prime factorization of any integer — displayed as a factor tree, exponential form, and expanded product. Check primality, count divisors, and find all factors.
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Prime Factorization
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Number
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Is Prime?
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# of Factors
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Distinct Primes
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ALL FACTORS
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Every integer > 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
Frequently Asked Questions
What is prime factorization?
Every integer greater than 1 can be expressed as a unique product of prime numbers. For example, 360 = 2³ × 3² × 5. This is guaranteed by the Fundamental Theorem of Arithmetic.
How many factors does a number have?
If n = p₁^a × p₂^b × p₃^c …, then the number of factors (divisors) = (a+1)(b+1)(c+1)… For example, 12 = 2² × 3¹ → (2+1)(1+1) = 6 factors: 1, 2, 3, 4, 6, 12.