Q1: Which of the following numbers is a prime number? (a) 9 (b) 15 (c) 11 (d) 21
Solution:
Ans: (c) Explanation: A prime number has exactly two factors: 1 and itself. The number \(11\) can only be divided evenly by \(1\) and \(11\), making it prime. The number \(9\) has factors \(1, 3, 9\); \(15\) has factors \(1, 3, 5, 15\); and \(21\) has factors \(1, 3, 7, 21\), so they are all composite numbers.
Q2: How many factors does the number 12 have? (a) 4 (b) 5 (c) 6 (d) 3
Solution:
Ans: (c) Explanation: The factors of \(12\) are the numbers that divide \(12\) evenly. These are: \(1, 2, 3, 4, 6, 12\). Counting them gives us 6 factors in total.
Q3: Which statement is true about the number 1? (a) 1 is a prime number (b) 1 is a composite number (c) 1 is neither prime nor composite (d) 1 is both prime and composite
Solution:
Ans: (c) Explanation: The number \(1\) is special. A prime number must have exactly two factors, but \(1\) has only one factor (itself). A composite number must have more than two factors. Since \(1\) doesn't fit either definition, it is neither prime nor composite.
Q4: Which number is a composite number? (a) 2 (b) 17 (c) 19 (d) 8
Solution:
Ans: (d) Explanation: A composite number has more than two factors. The number \(8\) has factors \(1, 2, 4, 8\), which is more than two factors. The numbers \(2, 17,\) and \(19\) are all prime numbers because they each have exactly two factors.
Q5: What is the smallest prime number? (a) 0 (b) 1 (c) 2 (d) 3
Solution:
Ans: (c) Explanation: The number \(2\) is the smallest prime number. It has exactly two factors: \(1\) and \(2\). The number \(0\) is not prime, \(1\) is neither prime nor composite, and \(3\) is prime but larger than \(2\).
Q6: Which of the following is NOT a factor of 18? (a) 6 (b) 9 (c) 4 (d) 3
Solution:
Ans: (c) Explanation: A factor divides the number evenly with no remainder. The factors of \(18\) are \(1, 2, 3, 6, 9, 18\). Since \(18 ÷ 4 = 4.5\) (not a whole number), \(4\) is not a factor of \(18\).
Q7: How many prime numbers are there between 1 and 10? (a) 3 (b) 4 (c) 5 (d) 2
Solution:
Ans: (b) Explanation: The prime numbers between \(1\) and \(10\) are: \(2, 3, 5, 7\). These four numbers each have exactly two factors. Therefore, there are 4 prime numbers between \(1\) and \(10\).
Q8: Which number below is the smallest composite number? (a) 2 (b) 3 (c) 4 (d) 6
Solution:
Ans: (c) Explanation: A composite number has more than two factors. The number \(4\) has factors \(1, 2, 4\) (three factors), making it composite. The numbers \(2\) and \(3\) are prime. The number \(6\) is composite but larger than \(4\). Therefore, \(4\) is the smallest composite number.
Section B: Fill in the Blanks
Q9: A number that has exactly two factors is called a __________ number.
Solution:
Ans: prime Explanation: A prime number is defined as a number greater than \(1\) that has exactly two factors: \(1\) and itself.
Q10: A number that has more than two factors is called a __________ number.
Solution:
Ans: composite Explanation: A composite number is a number greater than \(1\) that has more than two factors, meaning it can be divided evenly by numbers other than just \(1\) and itself.
Q11: The only even prime number is __________.
Solution:
Ans: 2 Explanation: The number \(2\) is the only even prime number because it has exactly two factors (\(1\) and \(2\)). All other even numbers have at least three factors, making them composite.
Q12: The number __________ is neither prime nor composite.
Solution:
Ans: 1 Explanation: The number \(1\) has only one factor (itself), so it doesn't meet the definition of prime (exactly two factors) or composite (more than two factors). Therefore, \(1\) is neither prime nor composite.
Q13: Numbers that divide evenly into another number are called __________.
Solution:
Ans: factors Explanation:Factors are numbers that divide into another number evenly, leaving no remainder. For example, the factors of \(12\) are \(1, 2, 3, 4, 6,\) and \(12\).
Q14: All prime numbers greater than 2 are __________ numbers.
Solution:
Ans: odd Explanation: Since \(2\) is the only even prime number, all other prime numbers cannot be even (or they would be divisible by \(2\)). Therefore, all prime numbers greater than \(2\) must be odd numbers.
Section C: Word Problems
Q15: Maria is making goodie bags for her party. She has 24 candies to share equally among the bags. List all the possible numbers of goodie bags she can make if she wants to use all the candies with none left over.
Solution:
Ans: Maria needs to find all the factors of \(24\). \(24 ÷ 1 = 24\) \(24 ÷ 2 = 12\) \(24 ÷ 3 = 8\) \(24 ÷ 4 = 6\) \(24 ÷ 6 = 4\) \(24 ÷ 8 = 3\) \(24 ÷ 12 = 2\) \(24 ÷ 24 = 1\) Final Answer: Maria can make 1, 2, 3, 4, 6, 8, 12, or 24 goodie bags
Q16: Jason says that 29 is a composite number because it is an odd number. Is Jason correct? Explain why or why not.
Solution:
Ans: Jason is not correct. A number being odd does not make it composite. To check if \(29\) is composite, we need to find its factors. The only factors of \(29\) are \(1\) and \(29\). Since \(29\) has exactly two factors, it is a prime number, not composite. Final Answer: No, Jason is not correct. 29 is a prime number because it has exactly two factors.
Q17: A teacher wants to arrange 17 students into equal rows for a class photo. What are all the possible arrangements she can make? What type of number is 17?
Solution:
Ans: To find the arrangements, we need the factors of \(17\). \(17 ÷ 1 = 17\) ✓ \(17 ÷ 17 = 1\) ✓ The factors of \(17\) are only \(1\) and \(17\). Possible arrangements: 1 row of 17 students, or 17 rows of 1 student each. Since \(17\) has exactly two factors, it is a prime number. Final Answer: 1 row of 17 students or 17 rows of 1 student; 17 is a prime number
Q18: Lisa wrote down all the prime numbers between 10 and 20. How many prime numbers did she write?
Solution:
Ans: Check each number between 10 and 20: \(11\): factors are \(1, 11\) → prime \(12\): factors are \(1, 2, 3, 4, 6, 12\) → composite \(13\): factors are \(1, 13\) → prime \(14\): factors are \(1, 2, 7, 14\) → composite \(15\): factors are \(1, 3, 5, 15\) → composite \(16\): factors are \(1, 2, 4, 8, 16\) → composite \(17\): factors are \(1, 17\) → prime \(18\): factors are \(1, 2, 3, 6, 9, 18\) → composite \(19\): factors are \(1, 19\) → prime The prime numbers are: \(11, 13, 17, 19\) Final Answer: Lisa wrote 4 prime numbers
Q19: Kevin has 36 baseball cards. He wants to organize them into equal groups with more than 1 card in each group and more than 1 group total. How many different ways can he organize his cards?
Solution:
Ans: Find all factors of \(36\): \(1, 2, 3, 4, 6, 9, 12, 18, 36\) We need to exclude arrangements with only 1 group or only 1 card per group. Exclude: \(1\) group of \(36\) cards and \(36\) groups of \(1\) card Valid factor pairs: \(2\) groups of \(18\) cards \(3\) groups of \(12\) cards \(4\) groups of \(9\) cards \(6\) groups of \(6\) cards \(9\) groups of \(4\) cards \(12\) groups of \(3\) cards \(18\) groups of \(2\) cards Final Answer: Kevin can organize his cards in 7 different ways
Q20: Sam thinks that all odd numbers are prime numbers. Give an example of an odd number that is NOT prime to show that Sam is wrong.
Solution:
Ans: An odd number that is NOT prime is a composite odd number. Example: \(9\) \(9\) is odd, but its factors are \(1, 3, 9\). Since \(9\) has more than two factors, it is composite, not prime. Other examples include: \(15, 21, 25, 27\) Final Answer: 9 (or 15, 21, 25, 27, etc.) is an odd composite number, showing Sam is wrong
The document Worksheet (with Solutions): Prime and Composite Numbers is a part of the Grade 4 Course Math Grade 4.
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