Prime Factorization

6.NOS.4 · Unit 1 · Lesson 1

Name   Period

Objectives / Objetivos

Content Objective: I can write a number as a product of its prime factors using a factor tree.

Language Objective: I can explain how I broke a number down using the words prime number, composite number, factor, and exponent.

Key Idea / Idea clave

Keep breaking a number apart until every factor is a prime number you cannot split anymore.

I Notice / Observo

  • What number are we breaking down into factors?
  • What's the difference between a factor and a prime factor?

I Wonder / Me pregunto

  • How many different ways can we start breaking 60 apart?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Prime number
Número primo		A number bigger than 1 that you can only divide by 1 and itself.
Un número mayor que 1 que solo se puede dividir entre 1 y sí mismo.
Composite number
Número compuesto		A number bigger than 1 that you can divide by more than just 1 and itself.
Un número mayor que 1 que se puede dividir entre más números, no solo 1 y sí mismo.
Prime factorization
Factorización prima		Writing a number as prime numbers multiplied together.
Escribir un número como números primos multiplicados.
Factor tree
Árbol de factores		A picture that splits a number into its prime numbers, step by step.
Un dibujo que separa un número en sus números primos, paso a paso.
Exponent
Exponente		A small number that tells how many times to multiply a number by itself.
Un número pequeño que dice cuántas veces multiplicar un número por sí mismo.

Practice Preview / Vista previa de práctica

  1. Which of the following is a prime number?
    1. 17
    2. 15
    3. 21
    4. 9
  2. Match each number to its prime factorization.
  3. Build the factor tree. Write each number as a product of primes.
  4. Find Marcus's Mistake
    1. Step 1: Find prime factorization of 48 — Start: 48
    2. Step 2: First split — 48 = 6 × 8
    3. Step 3: Break down 6 — 6 = 2 × 3
    4. Step 4: Break down 8 — 8 = 2 × 4
    5. Step 5: Final answer — 48 = 2 × 3 × 2 × 4

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: