Prime Factorization
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
Prime Factorization & Factor Trees. 1. Prime Number: Has exactly two factors (1 and itself, e.g. 2, 3, 5, 7, 11). 2. Split composite number into factor pairs until every branch ends in a prime. 3. Write final product using exponents in ascending order (e.g. 60 = 2² × 3 × 5)
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 / Término | Definition / Definición |
|---|---|
| Prime Factorization Factorización prima | Writing a whole number as a product of only prime numbers. Escribir un número entero como un producto de solo números primos. |
| 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. |
| Factor Factor | A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4. Un factor de un número entero lo divide exactamente, sin dejar residuo. Por ejemplo, 3 es un factor de 12 porque 12 ÷ 3 = 4. |
| 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
Read each task. Show your work in the spaces provided and explain how you know.
1. Which of the following is a prime number?
- A 9
- B 15
- C 17
- D 21
Answer:
2. Match each number to its prime factorization.
Write the letter of the matching item in the blank.
| 1. | 12 | A. | 3 × 3 × 5 | |
| 2. | 18 | B. | 2 × 3 × 3 | |
| 3. | 20 | C. | 2 × 2 × 7 | |
| 4. | 28 | D. | 2 × 5 × 5 | |
| 5. | 45 | E. | 2 × 2 × 5 | |
| 6. | 50 | F. | 2 × 2 × 3 |
3. Build the factor tree. Write each number as a product of primes.
Complete each empty cell. Show your reasoning below.
| Number | First Split | Prime Factorization |
|---|---|---|
| 24 | ||
| 36 | ||
| 40 | ||
| 56 |
4. Find Marcus's Mistake
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: