Exploring Factor Trees and GCF/LCM Shortcuts

In this video, Brett Berry introduces the concept of factor trees, explaining how they can be used to break down numbers into their prime components. He demonstrates creating factor trees for numbers 45 and 120, and shows how these can be used to find the greatest common factor (GCF) and least common multiple (LCM). Additionally, Brett explains how factor trees can simplify fractions and radicals, providing a practical tool for various mathematical operations.

What is the main purpose of using factor trees?

• To add large numbers

• To break down large numbers into their prime components

• To divide large numbers

• To multiply large numbers

Which of the following is a prime factor of 45?

• 9

• 5

• 10

• 12

What is the prime factorization of 120?

• 2^2 * 3^2 * 5

• 2 * 3^2 * 5

• 2^3 * 3^2 * 5

• 2^3 * 3 * 5

How do you find the greatest common factor (GCF) using factor trees?

• By adding the prime factors of both numbers

• By multiplying the common prime factors of both numbers

• By dividing the prime factors of both numbers

• By subtracting the prime factors of both numbers

What is the GCF of 45 and 120?

• 20

• 15

• 10

• 5

How do you find the least common multiple (LCM) using factor trees?

• By multiplying the smallest prime factors of both numbers

• By dividing the prime factors of both numbers

• By adding the prime factors of both numbers

• By multiplying the largest prime factors of both numbers

What is the LCM of 45 and 120?

• 180

• 480

• 240

• 360

How can factor trees help in reducing fractions?

• By adding the prime factors of the numerator and denominator

• By multiplying the prime factors of the numerator and denominator

• By canceling out common prime factors in the numerator and denominator

• By dividing the prime factors of the numerator and denominator

What is the simplified form of the fraction 45/120?

• 3/8

• 3/4

• 5/8

• 5/9

How can factor trees be used to simplify cube roots?

• By dividing the prime factors

• By splitting the prime factors into separate roots and canceling out the cube root with the cube power

• By multiplying the prime factors

• By adding the prime factors