Prime Numbers Practice Exercises (With Answers)

📚 Topic Summary

Prime numbers are the building blocks of all whole numbers. A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Understanding prime numbers is essential for many areas of mathematics, including cryptography and number theory. Let's test your knowledge with these exercises!

🧠 Part A: Vocabulary

Match the following terms with their definitions:

1. Prime Number
2. Composite Number
3. Divisor
4. Factor
5. Greatest Common Factor (GCF)

1. A whole number greater than 1 that has more than two divisors.
2. A number that divides evenly into another number.
3. The largest factor that two or more numbers share.
4. A number that is multiplied by another number to get a product.
5. A whole number greater than 1 that has only two divisors: 1 and itself.

✏️ Part B: Fill in the Blanks

Complete the following sentences:

A prime number is only divisible by 1 and _______. The first few prime numbers are 2, 3, _______, 7, and 11. A number that is not prime is called a _______ number. Finding the prime _______ of a number means breaking it down into its prime factors. The number 1 is neither prime nor _______.

🤔 Part C: Critical Thinking

Explain in your own words why 1 is not considered a prime number.

✅ Answer Key

Part A: Vocabulary

• 🔍 Prime Number: A whole number greater than 1 that has only two divisors: 1 and itself.
• 💡 Composite Number: A whole number greater than 1 that has more than two divisors.
• 📝 Divisor: A number that divides evenly into another number.
• 🧮 Factor: A number that is multiplied by another number to get a product.
• 🌱 Greatest Common Factor (GCF): The largest factor that two or more numbers share.

Part B: Fill in the Blanks

• 1️⃣ A prime number is only divisible by 1 and itself.
• 2️⃣ The first few prime numbers are 2, 3, 5, 7, and 11.
• 3️⃣ A number that is not prime is called a composite number.
• 4️⃣ Finding the prime factorization of a number means breaking it down into its prime factors.
• 5️⃣ The number 1 is neither prime nor composite.

Part C: Critical Thinking

• 🌱 1 is not considered a prime number because prime numbers, by definition, must have exactly two distinct positive divisors: 1 and themselves. The number 1 only has one divisor, which is 1 itself. Therefore, it doesn't meet the criteria to be classified as a prime number.