Prime Factors Worksheet for Kids - Multiple Choice Questions on Prime Factorization

Let's solve each problem step by step:

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Problem 1:

Question: \(2^3 \times 7\) is the prime factorization of which number?
- Options: a. 42, b. 56, c. 28, d. none of these

Solution:
- Calculate \(2^3 \times 7\):
\[
2^3 = 8
\]
\[
8 \times 7 = 56
\]
- Therefore, \(2^3 \times 7\) is the prime factorization of 56.

Answer: b. 56

---

Problem 2:

Question: What is the prime factorization of 110?
- Options: a. \(5^2 \times 11\), b. \(2^5 \times 11\), c. \(5 \times 22\), d. \(2 \times 5 \times 11\)

Solution:
- Start with 110 and break it down into prime factors:
\[
110 \div 2 = 55 \quad (\text{2 is a prime factor})
\]
\[
55 \div 5 = 11 \quad (\text{5 is a prime factor})
\]
\[
11 \div 11 = 1 \quad (\text{11 is a prime factor})
\]
- The prime factorization of 110 is:
\[
2 \times 5 \times 11
\]

Answer: d. \(2 \times 5 \times 11\)

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Problem 3:

Question: What is the prime factorization of 99?
- Options: a. \(3^2 \times 11\), b. \(3^3 \times 11\), c. \(9 \times 22\), d. all of these

Solution:
- Start with 99 and break it down into prime factors:
\[
99 \div 3 = 33 \quad (\text{3 is a prime factor})
\]
\[
33 \div 3 = 11 \quad (\text{3 is a prime factor again})
\]
\[
11 \div 11 = 1 \quad (\text{11 is a prime factor})
\]
- The prime factorization of 99 is:
\[
3^2 \times 11
\]

Answer: a. \(3^2 \times 11\)

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Problem 4:

Question: What is the prime factorization of 93?
- Options: a. \(3 \times 30\), b. \(3 \times 31\), c. \(3 \times 3 \times 3 \times 3\), d. 0

Solution:
- Start with 93 and break it down into prime factors:
\[
93 \div 3 = 31 \quad (\text{3 is a prime factor})
\]
\[
31 \div 31 = 1 \quad (\text{31 is a prime factor})
\]
- The prime factorization of 93 is:
\[
3 \times 31
\]

Answer: b. \(3 \times 31\)

---

Problem 5:

Question: The prime factors of 70 are:
- Options: a. \(2 \times 3 \times 5 \times 7\), b. \(2 \times 2 \times 5\), c. \(2 \times 3 \times 5\), d. \(2 \times 5 \times 7\)

Solution:
- Start with 70 and break it down into prime factors:
\[
70 \div 2 = 35 \quad (\text{2 is a prime factor})
\]
\[
35 \div 5 = 7 \quad (\text{5 is a prime factor})
\]
\[
7 \div 7 = 1 \quad (\text{7 is a prime factor})
\]
- The prime factorization of 70 is:
\[
2 \times 5 \times 7
\]

Answer: d. \(2 \times 5 \times 7\)

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Problem 6:

Question: The prime factors of 440 are:
- Options: a. \(2 \times 5 \times 7\), b. \(2 \times 3 \times 5 \times 5\), c. \(2 \times 2 \times 2 \times 5 \times 11\), d. \(2 \times 3 \times 3 \times 5 \times 5\)

Solution:
- Start with 440 and break it down into prime factors:
\[
440 \div 2 = 220 \quad (\text{2 is a prime factor})
\]
\[
220 \div 2 = 110 \quad (\text{2 is a prime factor again})
\]
\[
110 \div 2 = 55 \quad (\text{2 is a prime factor again})
\]
\[
55 \div 5 = 11 \quad (\text{5 is a prime factor})
\]
\[
11 \div 11 = 1 \quad (\text{11 is a prime factor})
\]
- The prime factorization of 440 is:
\[
2 \times 2 \times 2 \times 5 \times 11
\]

Answer: c. \(2 \times 2 \times 2 \times 5 \times 11\)

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Problem 7:

Question: The prime factors of 40 are:
- Options: a. \(2 \times 2 \times 3 \times 5 \times 5\), b. \(2 \times 3 \times 5 \times 5\), c. \(2 \times 2 \times 2 \times 5\), d. \(2 \times 3 \times 5\)

Solution:
- Start with 40 and break it down into prime factors:
\[
40 \div 2 = 20 \quad (\text{2 is a prime factor})
\]
\[
20 \div 2 = 10 \quad (\text{2 is a prime factor again})
\]
\[
10 \div 2 = 5 \quad (\text{2 is a prime factor again})
\]
\[
5 \div 5 = 1 \quad (\text{5 is a prime factor})
\]
- The prime factorization of 40 is:
\[
2 \times 2 \times 2 \times 5
\]

Answer: c. \(2 \times 2 \times 2 \times 5\)

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Problem 8:

Question: _________ is the prime factorization of 24.
- Options: a. \(2 \times 2 \times 2 \times 3\), b. \(2 \times 2 \times 2\), c. \(2 \times 2 \times 2 \times 2 \times 3\), d. \(2 \times 2 \times 3 \times 3\)

Solution:
- Start with 24 and break it down into prime factors:
\[
24 \div 2 = 12 \quad (\text{2 is a prime factor})
\]
\[
12 \div 2 = 6 \quad (\text{2 is a prime factor again})
\]
\[
6 \div 2 = 3 \quad (\text{2 is a prime factor again})
\]
\[
3 \div 3 = 1 \quad (\text{3 is a prime factor})
\]
- The prime factorization of 24 is:
\[
2 \times 2 \times 2 \times 3
\]

Answer: a. \(2 \times 2 \times 2 \times 3\)

---

Problem 9:

Question: Which of the following contains all prime numbers?
- Options: a. \(2, 3, 5, 7, 11\), b. \(2, 3, 5, 7, 9\), c. \(2, 4, 5, 7, 11\), d. \(2, 3, 5, 7, 12\)

Solution:
- Check each option:
- Option a: \(2, 3, 5, 7, 11\) — All are prime numbers.
- Option b: \(2, 3, 5, 7, 9\) — 9 is not a prime number (it is \(3 \times 3\)).
- Option c: \(2, 4, 5, 7, 11\) — 4 is not a prime number (it is \(2 \times 2\)).
- Option d: \(2, 3, 5, 7, 12\) — 12 is not a prime number (it is \(2 \times 2 \times 3\)).

Answer: a. \(2, 3, 5, 7, 11\)

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Problem 10:

Question: The prime factor of 15 is:
- Options: a. \(3 \times 5\), b. \(15 \times 1\), c. \(3 \times 5 \times 5\), d. \(3 \times 5 \times 2\)

Solution:
- Start with 15 and break it down into prime factors:
\[
15 \div 3 = 5 \quad (\text{3 is a prime factor})
\]
\[
5 \div 5 = 1 \quad (\text{5 is a prime factor})
\]
- The prime factorization of 15 is:
\[
3 \times 5
\]

Answer: a. \(3 \times 5\)

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Final Answers:

1. b. 56
2. d. \(2 \times 5 \times 11\)
3. a. \(3^2 \times 11\)
4. b. \(3 \times 31\)
5. d. \(2 \times 5 \times 7\)
6. c. \(2 \times 2 \times 2 \times 5 \times 11\)
7. c. \(2 \times 2 \times 2 \times 5\)
8. a. \(2 \times 2 \times 2 \times 3\)
9. a. \(2, 3, 5, 7, 11\)
10. a. \(3 \times 5\)

\boxed{b, d, a, b, d, c, c, a, a, a}