Recognizing prime and composite numbers | Factors and multiples | Pre-Algebra | Khan Academy

TL;DR

Determine if a number is prime, composite, or neither based on its factors.

Transcript

Determine whether the following numbers are prime, composite, or neither. So just as a bit of review, a prime number is a natural number-- so one of the counting numbers, 1, 2, 3, 4, 5, 6, so on and so forth-- that has exactly two factors. So its factors are 1 and itself. So an example of a prime factor is 3. There's only two natural numbers that a... Read More

Key Insights

• 🧑‍🏭 Prime numbers have only two factors: 1 and themselves.
• #️⃣ Composite numbers have more than two factors and can be divided evenly by multiple natural numbers.
• #️⃣ The number 2 is the only even prime number.
• 🧑‍🏭 1 is neither prime nor composite because it has only one factor.
• 🧑‍🏭 Understanding the factors of a number helps in determining whether it is prime, composite, or neither.
• #️⃣ Prime numbers play a significant role in number theory and cryptography.
• 🧑‍🏭 Composite numbers have a variety of factors and can be further broken down into prime factors.

Questions & Answers

Q: What defines a prime number?

A prime number is a natural number that has exactly two factors: 1 and itself. It cannot be divided evenly by any other natural number.

Q: How do you determine if a number is composite?

A composite number is a natural number that has more than just 1 and itself as factors. It can be divided evenly by other natural numbers, resulting in more than two factors.

Q: Can you provide an example of a composite number?

Sure! Let's take the number 24. It can be evenly divided by 1, 2, 3, 4, 6, 8, 12, and 24. Since it has more factors than just 1 and itself, it is classified as a composite number.

Q: What is the difference between prime and composite numbers?

The main difference is found in the number of factors. Prime numbers have only two factors, while composite numbers have more than two. This distinction determines their classification.

Summary & Key Takeaways

• Prime numbers have exactly two factors: 1 and itself.

• Composite numbers have more than two factors.

• Neither prime nor composite numbers have only one factor or do not meet the criteria for being composite.