What process involves breaking down a number until only prime numbers are left?

What process involves breaking down a number until only prime numbers are left?

• A. Factorization
• B. Multiplication
• C. Prime Factorization
• D. Division

Answer: (C)

Prime factorization is the process of breaking down a number into its prime factors—those prime numbers that, when multiplied together in various combinations, will result in the original number. For example, to find the prime factorization of 18, one would break it down into 2 and 3, because 2 × 3 × 3 equals 18, where 2 and 3 are both prime numbers. This process is crucial in various areas of mathematics, such as simplifying fractions, finding the least common multiple (LCM), or determining greatest common divisors (GCD). In contrast, the other processes listed do not specifically focus on identifying prime components of numbers. Factorization generally refers to the broader concept of expressing a number as a product of other numbers, which may include non-prime factors. Multiplication is simply the arithmetic operation of combining numbers to get a product, and division is about determining how many times one number is contained within another. Therefore, prime factorization specifically hones in on the analysis of a number down to its fundamental building blocks—prime numbers—making it the correct choice in this context.

Prime factorization is the process of breaking down a number into its prime factors—those prime numbers that, when multiplied together in various combinations, will result in the original number. For example, to find the prime factorization of 18, one would break it down into 2 and 3, because 2 × 3 × 3 equals 18, where 2 and 3 are both prime numbers.

This process is crucial in various areas of mathematics, such as simplifying fractions, finding the least common multiple (LCM), or determining greatest common divisors (GCD). In contrast, the other processes listed do not specifically focus on identifying prime components of numbers. Factorization generally refers to the broader concept of expressing a number as a product of other numbers, which may include non-prime factors. Multiplication is simply the arithmetic operation of combining numbers to get a product, and division is about determining how many times one number is contained within another. Therefore, prime factorization specifically hones in on the analysis of a number down to its fundamental building blocks—prime numbers—making it the correct choice in this context.