Prime Factorization
Find prime factorizations in Grade 6 math using factor trees or repeated division — express composite numbers as products of prime factors and apply to finding GCF and LCM.
Key Concepts
Property When we write a composite number as a product of its prime factors, we have written the prime factorization of the number. For example, the prime factorization of 8 is $2 \cdot 2 \cdot 2$.
Examples $12 = 2 \cdot 2 \cdot 3$ $20 = 2 \cdot 2 \cdot 5$ $45 = 3 \cdot 3 \cdot 5$.
Explanation Think of it as a secret recipe! Every whole number bigger than 1 is either prime or can be built by multiplying primes. Finding the prime factorization means discovering that unique set of prime number ingredients. You must break the number all the way down until only prime pieces are left, no composites allowed!
Common Questions
What is prime factorization?
Prime factorization breaks a composite number into a product of prime numbers. For example, 36 equals 2 times 2 times 3 times 3, written as 2 squared times 3 squared. Every composite number has exactly one prime factorization.
How do you build a factor tree?
Start with the number and find any two factors. If a factor is composite, split it again. Continue until all branches end in prime numbers. The primes at all branch tips form the prime factorization of the original number.
What are prime numbers?
A prime number has exactly two factors: 1 and itself. Examples include 2, 3, 5, 7, 11, and 13. The number 1 is not prime because it has only one factor. The number 2 is the only even prime number.
How is prime factorization used in math?
Prime factorization is used to find the GCF and LCM of numbers, which helps simplify fractions and find common denominators. It builds foundational understanding for algebraic topics in middle and high school.