Prime Factorization Explained!

Summary

This video explains the difference between prime and composite numbers, covering their definitions and examples. Prime numbers can only be divided by 1 and themselves, while composite numbers can be broken down into smaller prime factors. The video also demonstrates prime factorization, showing how to decompose larger numbers into their prime components using methods like factor trees. Examples include prime factorizations of 50, 120, 280, 540, and 10,800, emphasizing the use of exponents for simpler expressions. The lesson concludes by reinforcing key concepts through practice exercises.

Takeaways

• 😀 Prime numbers can only be divided by 1 and themselves, while composite numbers can be factored into smaller prime numbers.
• 😀 5 is a prime number, as it can only be divided by 1 and 5, whereas 8 is a composite number because it can be broken down into 2 × 2 × 2.
• 😀 Zero and one are neither prime nor composite numbers.
• 😀 The prime factorization of a number is breaking it down into the product of prime numbers.
• 😀 7 is a prime number, while 10 is a composite number because it can be factored as 2 × 5.
• 😀 Prime numbers include: 2, 3, 5, 7, 11, 13, 17, 19, etc. Composite numbers include: 4, 6, 8, 9, 10, 12, 14, 15, etc.
• 😀 All prime numbers have 1 as one of their factors, and composite numbers do not.
• 😀 The prime factorization of 50 is 2 × 5 × 5, or 2 × 5².
• 😀 The prime factorization of 120 is 2³ × 3 × 5.
• 😀 Using the factor tree method, 10,800 can be broken down into its prime factors as 2⁴ × 3³ × 5².

Q & A

What is the main difference between prime and composite numbers?

A prime number is a number greater than 1 that can only be divided by 1 and itself, while a composite number has more than two factors, meaning it can be divided by numbers other than 1 and itself.

Can you give an example of a prime number?

An example of a prime number is 5, because its only factors are 1 and 5.

What is a composite number? Can you give an example?

A composite number is a number that has more than two factors. For example, 8 is composite because it can be broken down into 2 × 2 × 2.

What does prime factorization mean?

Prime factorization is the process of breaking down a number into the product of prime numbers that multiply to give the original number.

How do you write prime factorizations using exponents?

You write prime factorizations using exponents when there are repeated prime factors. For example, the prime factorization of 50 is 2 × 5 × 5, which can be written as 2 × 5².

What is the prime factorization of 120?

The prime factorization of 120 is 2³ × 3 × 5.

Why is 7 considered a prime number?

7 is a prime number because it only has two factors: 1 and 7.

How would you break down the number 50 using a factor tree?

To break down 50 using a factor tree, start by dividing by 2 (smallest prime), which gives 25. Then divide 25 by 5, which gives 5. Therefore, 50 = 2 × 5 × 5, or 2 × 5².

What is the prime factorization of 540 using the factor tree method?

The prime factorization of 540 using the factor tree method is 2² × 3³ × 5.

How can you verify the accuracy of your prime factorization?

You can verify the accuracy of your prime factorization by multiplying the prime factors back together. For example, 2⁴ × 3³ × 5 = 10,800, so the prime factorization is correct.