Prime Factorization of Numbers
Find prime factorization by dividing a number by prime factors until only 1 remains. Use factor trees or repeated division in Grade 9 number theory.
Key Concepts
Property Writing a composite number as a product of only prime numbers. For example, the prime factorization of 6 is $2 \cdot 3$.
Examples $120 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5$ $924 = 2 \cdot 2 \cdot 3 \cdot 7 \cdot 11$.
Explanation Think of it as cracking a code to find a number's prime building blocks! You can use a factor tree or division by primes to find these core ingredients. No matter how you start, you'll always end with the same unique set of prime factors for any given number.
Common Questions
What is the first step when prime factorization of numbers?
Always check for a greatest common factor (GCF) first. Factor out the GCF before applying grouping or special product patterns.
How do you verify factoring is correct?
Multiply your factors back together using distribution. If the product matches the original polynomial exactly, the factoring is correct.
When is factoring used in algebra?
Factoring solves quadratic equations, simplifies rational expressions, and finds zeros of polynomial functions in Grade 9 algebra.