Prime Factorization Concepts and Problems

The video tutorial explains the process of prime factorization, which involves breaking down an integer into its prime factors. It demonstrates this process with examples, including the numbers 16, 80, and 312, showing how to divide each by prime numbers until only prime numbers remain. The tutorial emphasizes the usefulness of prime factorization in various mathematical contexts.

What is the purpose of prime factorization?

• To multiply prime numbers to get a smaller integer

• To add prime numbers to get a larger integer

• To break down an integer into its prime factors

• To find the sum of prime numbers

Which number is the easiest to start dividing with when finding prime factors?

• Seven

• Two

• Three

• Five

What is the prime factorization of 16?

• 2 * 2 * 4

• 2 * 2 * 2 * 2

• 2 * 8

• 4 * 4

When dividing 80 by 2 repeatedly, what is the last prime number you reach?

• Twenty

• Ten

• Five

• Two

What is the prime factorization of 80?

• 4 * 4 * 5

• 2 * 4 * 5

• 2 * 2 * 2 * 10

• 2 * 2 * 2 * 2 * 5

Which prime number is used after 2 when finding the prime factors of 312?

• Three

• Five

• Seven

• Eleven

What is the prime factorization of 312?

• 2 * 2 * 2 * 3 * 13

• 2 * 2 * 3 * 13

• 2 * 3 * 13

• 2 * 2 * 2 * 2 * 13

Why is it important to only divide by prime numbers during factorization?

• To find the largest possible factors

• To make the process faster

• To ensure the result is a composite number

• To accurately break down the integer into its prime components

What is the first step in finding the prime factorization of an even number?

• Divide by three

• Divide by two

• Add two

• Multiply by two

Which of the following is a prime number?

• Sixteen

• Thirteen

• Nine

• Four