Understanding the Greatest Common Factor

The video tutorial explains the concept of the greatest common factor (GCF) using a practical example involving Carl, who wants to feed his rabbits equal portions of vegetables. It demonstrates how to find the GCF of two numbers by listing their factors and identifying the largest common one. The tutorial also shows how this concept can be applied to larger numbers, making problem-solving easier. The use of the distributive property in equations is highlighted to reinforce understanding.

What is the greatest common factor of two numbers?

• The sum of the two numbers

• The smallest number that divides both numbers

• The difference between the two numbers

• The largest number that divides both numbers

Why couldn't Carl feed six rabbits with the vegetables he had?

• He had more than enough vegetables for six rabbits

• He had exactly enough vegetables for six rabbits

• He didn't have enough vegetables for six rabbits

• He had too many vegetables

How many rabbits can Carl feed equally with his vegetables?

• Two rabbits

• One rabbit

• Three rabbits

• Four rabbits

What are the factors of six?

• 1, 2, 3, 6

• 1, 2, 4, 6

• 2, 3, 4, 6

• 1, 3, 5, 6

What is the greatest common factor of six and eight?

• Four

• Three

• Two

• One

How many pieces of broccoli and carrots does Carl have in the larger example?

• 50 broccoli and 100 carrots

• 45 broccoli and 90 carrots

• 60 broccoli and 120 carrots

• 30 broccoli and 60 carrots

How many rabbits can Carl feed with 45 broccoli pieces and 90 carrots?

• 30 rabbits

• 90 rabbits

• 60 rabbits

• 45 rabbits

What is the equation that represents the distribution of vegetables to rabbits in the larger example?

• 45 + 90 = 45 groups of 2 + 3

• 45 + 90 = 45 groups of 4 + 5

• 45 + 90 = 45 groups of 3 + 4

• 45 + 90 = 45 groups of 1 + 2

Why is understanding the greatest common factor important?

• It simplifies multiplication

• It helps in adding large numbers

• It is used in subtraction

• It makes solving problems with large numbers easier

What property is applied to the expression 45 times the quantity 1 plus 2?

• Associative property

• Identity property

• Commutative property

• Distributive property