Prime and Composite

Grade 4 · mathematics · 69 practice problems · read aloud

🔊 Listen to this explanation

Prime and Composite Numbers

🔍 What Are They?

A prime number is a whole number greater than 1 with exactly two factors: 1 and itself. A composite number is a whole number greater than 1 with more than two factors. The number 1 is special—it's neither prime nor composite!

Knowing this helps us understand number patterns, simplifies fractions, and is the foundation for more advanced math!

📝 How to Figure It Out: A Step-by-Step Guide

  1. Pick a number greater than 1.
  2. Find all its factors—the numbers that divide into it evenly.
  3. Count the factors:
    • If it has exactly two factors (1 and itself), it's PRIME.
    • If it has more than two factors, it's COMPOSITE.

✨ Visual Examples

Example 1: Is 7 a prime or composite number?

Let's find the factors of 7:

1 x 7 = 7. That's it!

Factors of 7: 1, 7

It has exactly two factors. ✅ 7 is PRIME.

Example 2: Is 12 a prime or composite number?

Let's find the factors of 12:

1 x 12 = 12, 2 x 6 = 12, 3 x 4 = 12.

Factors of 12: 1, 2, 3, 4, 6, 12

It has more than two factors. ✅ 12 is COMPOSITE.

⚠️ Common Mistakes to Avoid

Mistake 1: Thinking 1 is a prime number.

Remember: 1 only has one factor (itself!), so it's neither prime nor composite.

Mistake 2: Thinking all odd numbers are prime.

Remember: 9 is odd, but its factors are 1, 3, and 9. That's three factors, so 9 is composite!

💡 Tips & Tricks

Memory Aid: "Prime is Proud" – A prime number stands proud and alone, only divisible by 1 and itself.

First Few Primes: Memorize the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19. (2 is the only even prime number!)

🎯 How to Practice

  • Factor Hunt: Write down numbers from 2 to 30. For each one, list all its factors and label it Prime or Composite.
  • Number Line Sort: Create a number line and put all the prime numbers in one color and composite numbers in another.
  • Flashcards: Make flashcards with a number on the front. On the back, write its factors and whether it's prime or composite.

Practice problems

6 of the 69, worked through step by step — try them before opening the answer.

1 Is 17 a prime number?

  1. A) yes
  2. B) no

Hint: A prime number has exactly two factors: 1 and itself. Check if any numbers between 2 and the number divide it evenly.

Show the answer

Answer: A) yes

  1. Understand the definition of a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
  2. Check for obvious cases. 17 is greater than 1, so it could be prime. It is not an even number (doesn't end in 0, 2, 4, 6, 8), so it is not divisible by 2. The sum of its digits is 1 + 7 = 8, which is not divisible by 3, so 17 is not divisible by 3. It does not end in 0 or 5, so it is not divisible by 5.
  3. Test division by all prime numbers less than the square root of 17. We need to check divisibility by all primes less than sqrt(17). Since sqrt(16) = 4 and sqrt(25) = 5, sqrt(17) is between 4 and 5. So we only need to test primes less than 5: 2 and 3. (We already eliminated 2 and 3 in Step 2, but let's verify with division). - 17 ÷ 2 = 8.5 (not an integer) - 17 ÷ 3 = 5.666... (not an integer)
  4. Since there are no divisors among the primes less than sqrt(17), we conclude 17 is prime. The only positive divisors of 17 are 1 and 17 itself. Final Answer: yes

Step-by-step solution to determine if 17 is prime:

2 Is 47 a prime number?

  1. A) no
  2. B) yes

Hint: A prime number has exactly two factors: 1 and itself. Check if any numbers between 2 and the number's square root divide it evenly.

Show the answer

Answer: B) yes

  1. Check for divisibility by small prime numbers. We test if 47 is divisible by 2, 3, 5, 7, 11, 13, etc., up to the square root of 47. The square root of 47 is approximately 6.855, so we only need to test primes less than or equal to 6.855. The primes in this range are 2, 3, and 5. (7 is greater than 6.855, but we will check it anyway to be thorough, since 7*7=49 is greater than 47, so 7 cannot be a factor.)
  2. Test divisibility by 2. A number is divisible by 2 if it is even. 47 is odd, so it is not divisible by 2.
  3. Test divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. The digits of 47 are 4 and 7. 4 + 7 = 11. 11 is not divisible by 3, so 47 is not divisible by 3.
  4. Test divisibility by 5. A number is divisible by 5 if its last digit is 0 or 5. The last digit of 47 is 7, so it is not divisible by 5.
  5. Test divisibility by 7. Divide 47 by 7. 7 * 6 = 42, and 47 - 42 = 5. Since there is a remainder (5), 47 is not divisible by 7.
  6. Since the square root of 47 is about 6.855, the next prime to test would be 11, but 11 is greater than 6.855. If a number has a factor, one of the factors must be less than or equal to its square root. We have tested all primes up to and including 7 (which is the largest prime less than the square root of 47) and found no divisors. Conclusion: Since 47 has no divisors other than 1 and 47, it is a prime number. ANSWER: yes

To determine if 47 is a prime number, we need to check if it has any divisors other than 1 and itself. A prime number is only divisible by 1 and the number itself.

3 Is 29 a prime number?

  1. A) no
  2. B) yes

Hint: A prime number has exactly two factors: 1 and itself. Check if any numbers between 2 and the number itself divide evenly into it.

Show the answer

Answer: B) yes

  1. Check for divisibility by small prime numbers. We test divisibility by primes less than the square root of 29. The square root of 29 is approximately 5.39, so we only need to test primes less than or equal to 5: 2, 3, and 5.
  2. Test divisibility by 2. A number is divisible by 2 if it is even. 29 is odd, so it is not divisible by 2.
  3. Test divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. The digits of 29 are 2 and 9. Their sum is 2 + 9 = 11. 11 is not divisible by 3, so 29 is not divisible by 3.
  4. Test divisibility by 5. A number is divisible by 5 if its last digit is 0 or 5. The last digit of 29 is 9, so it is not divisible by 5.
  5. Conclusion. Since 29 is not divisible by any prime number less than or equal to 5 (which are 2, 3, and 5), and we have tested all possible divisors up to the square root of 29, we conclude that 29 has no divisors other than 1 and itself. Therefore, 29 is a prime number. ANSWER: yes

To determine if 29 is a prime number, we need to check if it has any divisors other than 1 and itself. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

4 Is 57 a prime number?

Hint: A prime number has exactly two factors: 1 and itself. Check if any number between 2 and the number's square root divides it evenly. Look at the digits: if the sum of the digits is divisible by 3, then the number is divisible by 3.

Show the answer

Answer: no

  1. A prime number has only two factors: 1 and itself. We need to check if 57 has any other factors.
  2. The square root of 57 is about 7.5, so we only need to test prime numbers up to 7: 2, 3, 5, and 7.
  3. Check divisibility by 2: 57 is odd, so it is not divisible by 2.
  4. Check divisibility by 3: The sum of the digits is 5 + 7 = 12. Since 12 is divisible by 3, 57 is divisible by 3.
  5. 57 ÷ 3 = 19. So 57 = 3 × 19. It has factors other than 1 and itself.
  6. Therefore, 57 is a composite number.

The answer is no.

5 Is 37 a prime number?

Hint: A prime number has exactly two factors: 1 and itself. Check if any number between 2 and the square root of the number divides it evenly.

Show the answer

Answer: yes

  1. A prime number has only two factors: 1 and itself.
  2. Find the square root of 37. sqrt(37) is about 6.08. So we only need to test prime numbers less than or equal to 6: 2, 3, and 5.
  3. Test divisibility by 2. 37 is odd, so it is not divisible by 2.
  4. Test divisibility by 3. Sum of digits: 3 + 7 = 10. 10 is not divisible by 3, so 37 is not divisible by 3.
  5. Test divisibility by 5. The last digit of 37 is 7, not 0 or 5, so it is not divisible by 5.
  6. Since no prime number less than or equal to sqrt(37) divides 37 evenly, 37 has no factors other than 1 and itself. Therefore, 37 is a prime number.

The answer is yes.

6 Is 62 a prime number or a composite number?

Hint: A prime number has exactly two factors: 1 and itself. A composite number has more than two factors. Check if 62 is divisible by any number other than 1 and 62.

Show the answer

Answer: composite

  1. A prime number has exactly two factors: 1 and itself. A composite number has more than two factors.
  2. Check if 62 is even. Since 62 ends in 2, it is an even number.
  3. Any even number greater than 2 is divisible by 2. 62 ÷ 2 = 31.
  4. This means 62 has factors 1, 2, 31, and 62 — that is four factors.
  5. Since 62 has more than two factors, it is a composite number.

The answer is composite.

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