Prime factorization | Factors and multiples | Pre-Algebra | Khan Academy

TL;DR

Learn how to find the prime factorization of a number and write it in exponential notation.

Transcript

Write the prime factorization of 75. Write your answer using exponential notation. So we have a couple of interesting things here. Prime factorization, and they say exponential notation. We'll worry about the exponential notation later. So the first thing we have to worry about is what is even a prime number? And just as a refresher, a prime number... Read More

Key Insights

• #️⃣ Prime numbers are only divisible by themselves and one, while composite numbers have multiple factors.
• #️⃣ Prime factorization breaks a number down into the product of prime numbers.
• 🧑‍🏭 Factorization trees help visualize the process of finding prime factors.
• 👻 Exponential notation allows writing repeated prime factors as exponents.

Questions & Answers

Q: What is a prime number?

A prime number is a number that is only divisible by itself and one. Examples include 2, 3, 5, and 7.

Q: How is prime factorization done?

Prime factorization involves breaking down a number into a product of prime numbers. You start with the smallest prime number and divide the number until you can no longer divide evenly.

Q: Why is 4 not a prime number?

4 is not a prime number because it is divisible by 2 and 1, making it a composite number.

Q: How do you write the prime factorization of 75 in exponential notation?

The prime factorization of 75 is 3 * 5 * 5. In exponential notation, it can be written as 3 * 5^2.

Summary & Key Takeaways

• A prime number is only divisible by itself and one, while a composite number can be divided by multiple factors.

• Prime factorization involves breaking down a number into a product of prime numbers.

• Using a factorization tree, you start with the smallest prime number and continue breaking down the number until you have only prime factors.