Prime Factorization

Enter a number to find its prime factorization. Prime factorization is the process of breaking down a number into the prime numbers that multiply together to make it.

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What is Prime Factorization?

Prime factorization is the process of finding which prime numbers multiply together to make the original number. Every positive integer greater than 1 can be expressed as a unique product of prime numbers (this is known as the Fundamental Theorem of Arithmetic).

For example, the prime factorization of 24 is 2³ × 3, which means 24 = 2 × 2 × 2 × 3.

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Why is Prime Factorization Useful?

Prime factorization is fundamental in number theory and has many practical applications:

• Finding the greatest common divisor (GCD) and least common multiple (LCM) of numbers
• Simplifying fractions
• Cryptography and computer security
• Understanding the structure of numbers

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