What is the difference between a prime number and a composite number?

A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself (e.g. 2, 3, 5, 7, 11). A composite number has more than two divisors and can be factored into smaller natural numbers.

Is 1 considered a prime number?

No. By mathematical definition, 1 is neither prime nor composite. It is the multiplicative unit.

What is a factor tree?

A factor tree is a visual diagram that branches a composite number into pairs of factors repeatedly until every final leaf node is a prime number.

Math

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Prime Factorization Calculator — Factor Tree & Prime Factors

Free prime factorization calculator. Find the prime factors of any positive integer, generate its factor tree, and calculate all divisors and exponential canonical form.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The Prime Factorization Calculator decomposes any positive integer into its fundamental multiplicative building blocks: prime numbers. It provides the exponential prime factorization, a visual factor tree, and a complete list of all divisors.

🔢 Integer to Factor

Enter any integer from 2 up to 9,007,199,254,740,991

Examples:

What is Prime Factorization Calculator — Factor Tree & Prime Factors?

How to use it

1️⃣ Enter any positive integer (e.g. 100, 360, 1024, or up to 15 digits).
2️⃣ Click one of the quick test numbers or press enter.
3️⃣ View the canonical prime factorization with exponents (e.g. 2² × 5²).
4️⃣ Inspect the hierarchical factor tree and complete list of all positive divisors.

Formula

Fundamental Theorem of Arithmetic: Every integer n > 1 can be uniquely represented as n = p₁ᵃ¹ × p₂ᵃ² × ... × pₖᵃᵏ, where pᵢ are distinct primes and aᵢ ≥ 1.

💡 See it in action — a real example

For the number 360: Prime Factors = 2³ × 3² × 5. Distinct primes: {2, 3, 5}. Total divisors: 24 (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360).

❓ Common questions

What is the difference between a prime number and a composite number?: A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself (e.g. 2, 3, 5, 7, 11). A composite number has more than two divisors and can be factored into smaller natural numbers.
Is 1 considered a prime number?: No. By mathematical definition, 1 is neither prime nor composite. It is the multiplicative unit.
What is a factor tree?: A factor tree is a visual diagram that branches a composite number into pairs of factors repeatedly until every final leaf node is a prime number.