The task involves identifying whether numbers are
prime or
composite. Let's solve each part of the problem step by step and explain the reasoning.
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Definitions:
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Prime Number: A number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
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Composite Number: A number greater than 1 that has more than two distinct positive divisors.
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Problem Solutions:
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a. Identify the numbers from the list below that are composite.
List: 2, 4, and 8
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2: The divisors of 2 are 1 and 2. Since it has exactly two divisors,
2 is prime.
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4: The divisors of 4 are 1, 2, and 4. Since it has more than two divisors,
4 is composite.
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8: The divisors of 8 are 1, 2, 4, and 8. Since it has more than two divisors,
8 is composite.
Answer: 4 and 8 are composite.
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####
b. Circle all the composite numbers in the list below.
List: 2, 6, 10, and 20
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2: As explained earlier,
2 is prime.
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6: The divisors of 6 are 1, 2, 3, and 6. Since it has more than two divisors,
6 is composite.
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10: The divisors of 10 are 1, 2, 5, and 10. Since it has more than two divisors,
10 is composite.
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20: The divisors of 20 are 1, 2, 4, 5, 10, and 20. Since it has more than two divisors,
20 is composite.
Answer: 6, 10, and 20 are composite.
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####
c. Is 19 a prime number?
To determine if 19 is prime:
- Check divisors of 19: The only divisors are 1 and 19.
- Since 19 has exactly two divisors,
19 is prime.
Answer: Yes, 19 is a prime number.
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####
d. If you “count by 3’s” for the number 37, will 37 be prime?
To determine if 37 is prime:
- Check divisors of 37: The only divisors are 1 and 37.
- Since 37 has exactly two divisors,
37 is prime.
Answer: Yes, 37 is prime.
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e. Are 3 and 9 prime or composite?
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3: The divisors of 3 are 1 and 3. Since it has exactly two divisors,
3 is prime.
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9: The divisors of 9 are 1, 3, and 9. Since it has more than two divisors,
9 is composite.
Answer: 3 is prime, and 9 is composite.
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f. Is 13 a prime or composite number?
To determine if 13 is prime:
- Check divisors of 13: The only divisors are 1 and 13.
- Since 13 has exactly two divisors,
13 is prime.
Answer: 13 is prime.
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g. Is 72 a prime or composite number?
To determine if 72 is prime:
- Check divisors of 72: The divisors include 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
- Since 72 has more than two divisors,
72 is composite.
Answer: 72 is composite.
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Final Answers:
1.
a. 4 and 8 are composite.
2.
b. 6, 10, and 20 are composite.
3.
c. Yes, 19 is a prime number.
4.
d. Yes, 37 is prime.
5.
e. 3 is prime, and 9 is composite.
6.
f. 13 is prime.
7.
g. 72 is composite.
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Boxed Final Answer:
\[
\boxed{
\text{a. 4 and 8 are composite.} \\
\text{b. 6, 10, and 20 are composite.} \\
\text{c. Yes, 19 is a prime number.} \\
\text{d. Yes, 37 is prime.} \\
\text{e. 3 is prime, and 9 is composite.} \\
\text{f. 13 is prime.} \\
\text{g. 72 is composite.}
}
\]
Parent Tip: Review the logic above to help your child master the concept of prime and composite numbers worksheet 5th grade.
