Find Factors and Multiples

6.NOS.4 · Unit 6 · Lesson 7

Name   Period

Objectives / Objetivos

Content Objective: I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.

Language Objective: I can explain my choice using the words factor, multiple, common, greatest, and least.

Key Idea / Idea clave

Greatest Common Factor (GCF) & Least Common Multiple (LCM). 1. GCF: Largest factor shared by two numbers — used to simplify fractions or divide into equal groups. 2. LCM: Smallest shared multiple — used to find common denominators. 3. Use prime factor trees or list method to find common factors/multiples

I Notice / Observo

  • I notice both quantities can be split into equal ___.
  • I notice some numbers appear in ___ lists.

I Wonder / Me pregunto

  • I wonder what the largest equal group size ___.

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Find Factors and Multiples
Hallar factores y múltiplos		Listing what divides a number evenly (its factors) and what it divides into evenly (its multiples), then finding what two numbers share.
Listar lo que divide un número exactamente (sus factores) y lo que el número forma al contar de esa cantidad (sus múltiplos), y luego hallar lo que dos números comparten.
Factor
Factor		A whole number that divides another number evenly, with no remainder.
Un número entero que divide a otro exactamente, sin residuo.
Multiple
Múltiplo		The result of multiplying a number by 1, 2, 3, and so on — where you land when you skip-count by it.
El resultado de multiplicar un número por 1, 2, 3, y así sucesivamente: donde caes al contar de esa cantidad.
Greatest common factor (GCF)
Máximo común divisor (MCD)		The largest number that is a factor of two or more numbers. It answers “how many equal groups can I make?”
El número más grande que es factor de dos o más números. Responde “¿cuántos grupos iguales puedo formar?”
Least common multiple (LCM)
Mínimo común múltiplo (mcm)		The smallest number that is a multiple of two or more numbers. It answers “when will these line up again?”
El número más pequeño que es múltiplo de dos o más números. Responde “¿cuándo volverán a coincidir?”
Factor pair
Par de factores		Two factors that multiply to make a number. In a word problem, one is the number of groups and the other is the size of each group.
Dos factores que se multiplican para formar un número. En un problema, uno es la cantidad de grupos y el otro el tamaño de cada grupo.

Practice Preview / Vista previa de práctica

  1. Which list shows all the factors of 12?
    1. 1, 2, 3, 4, 6, 12
    2. 12, 24, 36, 48
    3. 1, 12
    4. 2, 3, 4, 6
  2. The store has 48 pencils and 36 notebooks. Complete the factor lists, then find the GCF.
  3. Using prime factors, 48 = 2 × 2 × 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3. What is their GCF?
    1. 12, from the shared 2 × 2 × 3
    2. 144, from multiplying all the primes
    3. 6, from one 2 and one 3
    4. 2, the only prime they share
  4. Find the error
    1. Step 1: Problem — Find the LCM of 6 and 8.
    2. Step 2: Step 1 — Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
    3. Step 3: Step 2 — Multiples of 8: 8, 16, 24, 32, 40, 48
    4. Step 4: Step 3 — Both lists contain 48, so the LCM is 48.

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

Reflection / Reflexión

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