What is the definition of prime factorization?
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Prime factorization is a mathematical process of breaking down a number into its unique prime factors. It involves finding the prime numbers that, when multiplied together, result in the original number. This representation is known as the prime factorization of a number.
To find the prime factorization of a number, follow these steps:
1. Start by dividing the number by the smallest prime number, which is 2. If the number is divisible by 2, divide it repeatedly until it's no longer divisible by 2. Record the number of times you divided by 2.
2. Move on to the next prime number, which is 3, and repeat the process. Divide the number by 3 until it's no longer divisible by 3. Again, record the number of times you divided by 3.
3. Continue this process with the next prime numbers (5, 7, 11, and so on) until the number is reduced to 1. Note that you only need to check prime numbers up to the square root of the number being factorized.
4. The result of this process is the prime factorization of the original number, represented as the product of prime factors raised to their respective exponents. For example, if you divided a number by 2 four times and by 3 two times, the prime factorization would be 2^4 * 3^2.
Prime factorization provides a unique way to express a number in terms of its prime components, helping in various mathematical calculations and problem-solving scenarios.