Prime factorization is finding which prime numbers multiply together to make a given number. Every whole number greater than 1 can be written as a product of prime numbers.
Prime numbers have only two factors: 1 and the number itself. Factorization means breaking a number down into smaller factors until only prime numbers remain.
A prime number has exactly two factors, 1 and itself. A composite number has more than two factors. Knowing the difference helps when finding prime factors.
The number 1 is neither prime nor composite because it has only one factor—1 itself.
To find the prime factors of a number, divide the number by the smallest prime number possible and continue dividing until all factors are prime.
Always begin dividing by the smallest prime number. Continue until all remaining factors are prime numbers.
A factor tree is a diagram that shows how a number can be broken down into its prime factors step by step. Each branch splits until only prime numbers remain.
A factor tree helps you organize your work and check that you found all the prime factors correctly.
Prime factorization is important because it helps in simplifying fractions, finding greatest common factors (GCF), and least common multiples (LCM).
Understanding prime factorization gives you the tools to solve more complex math problems like finding GCFs and LCMs with confidence.