Problem Analysis and Solution
The worksheet focuses on understanding
factors,
multiples,
prime numbers, and
composite numbers. Let's solve each section step by step.
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Section A: True or False Statements
1.
Prime numbers have more than two factors.
-
False: By definition, a prime number has exactly
two factors: 1 and itself. For example, the prime number 7 has factors 1 and 7.
2.
15 is a multiple of 3.
-
True: A multiple of 3 is any number that can be expressed as \(3 \times n\), where \(n\) is an integer. Here, \(15 = 3 \times 5\), so 15 is a multiple of 3.
3.
2 and 3 are factors of 6.
-
True: The factors of 6 are the numbers that divide 6 without leaving a remainder. The factors of 6 are 1, 2, 3, and 6. Both 2 and 3 are indeed factors of 6.
4.
Composite numbers have more than two factors.
-
True: By definition, a composite number has more than two factors. For example, the number 4 is composite because its factors are 1, 2, and 4.
5.
12 is a prime number.
-
False: The number 12 is not a prime number because it has more than two factors (1, 2, 3, 4, 6, 12). Prime numbers have exactly two factors: 1 and themselves.
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####
Section B: Place Each Multiple in the Correct Column for Its Factor
We are given the numbers:
49, 64, 25, 44, 9, 66 and the factors:
4, 7, 6, 8, 3, 5. We need to determine which of these numbers are multiples of the given factors.
1.
Factor: 4
- Multiples of 4: Numbers divisible by 4.
- From the list:
64 (since \(64 \div 4 = 16\)).
- Answer:
64
2.
Factor: 7
- Multiples of 7: Numbers divisible by 7.
- From the list:
49 (since \(49 \div 7 = 7\)).
- Answer:
49
3.
Factor: 6
- Multiples of 6: Numbers divisible by 6.
- From the list:
66 (since \(66 \div 6 = 11\)).
- Answer:
66
4.
Factor: 8
- Multiples of 8: Numbers divisible by 8.
- From the list:
64 (since \(64 \div 8 = 8\)).
- Answer:
64
5.
Factor: 3
- Multiples of 3: Numbers divisible by 3.
- From the list:
44 (not divisible by 3),
9 (since \(9 \div 3 = 3\)),
66 (already placed under factor 6).
- Answer:
9
6.
Factor: 5
- Multiples of 5: Numbers divisible by 5.
- From the list:
25 (since \(25 \div 5 = 5\)).
- Answer:
25
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####
Section C: Which Number in Each Row Is NOT a Prime Number?
We are given rows of three numbers and need to identify which number in each row is
not a prime number.
1.
Row a): 3, 5, 10
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3: Prime (factors: 1, 3).
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5: Prime (factors: 1, 5).
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10: Not prime (factors: 1, 2, 5, 10).
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Answer: 10
2.
Row b): 16, 2, 7
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16: Not prime (factors: 1, 2, 4, 8, 16).
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2: Prime (factors: 1, 2).
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7: Prime (factors: 1, 7).
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Answer: 16
3.
Row c): 11, 21, 23
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11: Prime (factors: 1, 11).
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21: Not prime (factors: 1, 3, 7, 21).
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23: Prime (factors: 1, 23).
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Answer: 21
4.
Row d): 8, 2, 19
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8: Not prime (factors: 1, 2, 4, 8).
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2: Prime (factors: 1, 2).
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19: Prime (factors: 1, 19).
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Answer: 8
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Final Answers
####
Section A: True or False
1. False
2. True
3. True
4. True
5. False
####
Section B: Place Each Multiple
- Factor 4: 64
- Factor 7: 49
- Factor 6: 66
- Factor 8: 64
- Factor 3: 9
- Factor 5: 25
####
Section C: Which Number Is NOT a Prime Number?
a) 10
b) 16
c) 21
d) 8
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Boxed Final Answer
\[
\boxed{
\text{A: False, True, True, True, False} \\
\text{B: 64, 49, 66, 64, 9, 25} \\
\text{C: 10, 16, 21, 8}
}
\]
Parent Tip: Review the logic above to help your child master the concept of factors and multiples worksheet.
