Factoring is the process of breaking down a number or expression into its constituent parts (factors) that, when multiplied together, produce the original number or expression. For numbers, this means finding prime numbers that multiply together to give the original number.
For example, the number 12 can be factored as 2 x 2 x 3 (prime factorization) or as 4 x 3 or 6 x 2. Factoring is a fundamental skill in algebra and is essential for simplifying expressions, solving equations, and finding common denominators.
Follow these steps to find the prime factorization of a number:
Every integer greater than 1 can be expressed as a unique product of prime powers. This is known as the Fundamental Theorem of Arithmetic.
Problem: Find the prime factorization of 84
Solution:
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, 11, 13, etc.
Prime factorization helps find the GCD and LCM of numbers, simplify fractions, and solve various algebraic problems. It is fundamental in number theory.
Yes, but typically we factor the absolute value and include -1 as a factor. For example, -12 = -1 × 2² × 3.