Q1: Which of the following numbers is a factor of 24? (a) 5 (b) 7 (c) 8 (d) 9
Solution:
Ans: (c) Explanation: A factor is a number that divides evenly into another number without a remainder. \(24 \div 8 = 3\), so 8 is a factor of 24. The numbers 5, 7, and 9 do not divide 24 evenly.
Q2: What is the greatest common factor (GCF) of 12 and 18? (a) 3 (b) 6 (c) 9 (d) 12
Solution:
Ans: (b) Explanation: The factors of 12 are: 1, 2, 3, 4, 6, 12 The factors of 18 are: 1, 2, 3, 6, 9, 18 The greatest common factor that appears in both lists is 6.
Q3: Which number is a multiple of 7? (a) 34 (b) 42 (c) 50 (d) 60
Solution:
Ans: (b) Explanation: A multiple is the result of multiplying a number by a whole number. \(7 \times 6 = 42\), so 42 is a multiple of 7. The other numbers are not divisible by 7.
Q4: What is the least common multiple (LCM) of 4 and 6? (a) 10 (b) 12 (c) 18 (d) 24
Solution:
Ans: (b) Explanation: The multiples of 4 are: 4, 8, 12, 16, 20... The multiples of 6 are: 6, 12, 18, 24... The least common multiple that appears in both lists is 12.
Q5: Which of the following numbers is a prime number? (a) 12 (b) 15 (c) 17 (d) 21
Solution:
Ans: (c) Explanation: A prime number has exactly two factors: 1 and itself. The number 17 can only be divided evenly by 1 and 17. The other numbers have more than two factors: 12 has factors 1, 2, 3, 4, 6, 12; 15 has factors 1, 3, 5, 15; and 21 has factors 1, 3, 7, 21.
Q6: Which of the following numbers is a composite number? (a) 2 (b) 7 (c) 11 (d) 20
Solution:
Ans: (d) Explanation: A composite number has more than two factors. The number 20 has factors 1, 2, 4, 5, 10, and 20, which is more than two factors. The numbers 2, 7, and 11 are prime numbers because they only have two factors each.
Q7: What are all the factors of 16? (a) 1, 2, 4, 8, 16 (b) 1, 2, 4, 16 (c) 2, 4, 8, 16 (d) 1, 4, 8, 16
Solution:
Ans: (a) Explanation:Factors are all the numbers that divide evenly into 16. \(16 \div 1 = 16\), \(16 \div 2 = 8\), \(16 \div 4 = 4\), \(16 \div 8 = 2\), \(16 \div 16 = 1\) So the complete list of factors is: 1, 2, 4, 8, 16.
Q8: Which pair of numbers has a GCF of 1? (a) 6 and 9 (b) 8 and 12 (c) 9 and 16 (d) 10 and 15
Solution:
Ans: (c) Explanation: When two numbers have a GCF of 1, they share no common factors except 1, and they are called relatively prime. Factors of 9: 1, 3, 9 Factors of 16: 1, 2, 4, 8, 16 The only common factor is 1. The other pairs share larger common factors: 6 and 9 share 3; 8 and 12 share 4; 10 and 15 share 5.
## Section B: Fill in the Blanks Q9: A number that has exactly two factors, 1 and itself, is called a __________ number.
Solution:
Ans: prime Explanation: A prime number is defined as having exactly two factors. Examples include 2, 3, 5, 7, 11, 13, and so on.
Q10: A number that is multiplied by another number to get a product is called a __________.
Solution:
Ans: factor Explanation: In multiplication, the numbers being multiplied together are called factors. For example, in \(3 \times 4 = 12\), both 3 and 4 are factors of 12.
Q11: The smallest multiple that two or more numbers share is called the __________ __________ __________.
Solution:
Ans: least common multiple Explanation: The least common multiple (LCM) is the smallest number that is a multiple of two or more given numbers. For example, the LCM of 3 and 4 is 12.
Q12: The number 1 is neither prime nor __________.
Solution:
Ans: composite Explanation: The number 1 is a special case. It only has one factor (itself), so it does not meet the definition of a prime number (which needs exactly two factors) or a composite number (which needs more than two factors).
Q13: The product of a number and any whole number is called a __________ of that number.
Solution:
Ans: multiple Explanation: A multiple is obtained by multiplying a number by whole numbers. For example, multiples of 5 are \(5 \times 1 = 5\), \(5 \times 2 = 10\), \(5 \times 3 = 15\), and so on.
Q14: The greatest factor that two or more numbers share is called the __________ __________ __________.
Solution:
Ans: greatest common factor Explanation: The greatest common factor (GCF) is the largest factor that appears in the factor lists of two or more numbers. For example, the GCF of 8 and 12 is 4.
## Section C: Word Problems Q15: Maria is making party bags for her birthday. She has 24 candies and 36 stickers. She wants to make the greatest number of identical party bags with no items left over. How many party bags can she make?
Solution:
Ans: To find the greatest number of identical bags, we need to find the GCF of 24 and 36. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 The GCF is 12. Final Answer: 12 party bags
Q16: A bakery makes both chocolate and vanilla cupcakes. Chocolate cupcakes are made in batches of 8, and vanilla cupcakes are made in batches of 12. What is the smallest number of each type of cupcake the bakery can make to have an equal number of both flavors?
Solution:
Ans: We need to find the LCM of 8 and 12. Multiples of 8: 8, 16, 24, 32, 40... Multiples of 12: 12, 24, 36, 48... The LCM is 24. Final Answer: 24 cupcakes of each flavor
Q17: Jason wants to arrange 18 toy cars into equal rows with no cars left over. What are all the possible numbers of rows he can make?
Solution:
Ans: To find all possible numbers of rows, we need to find all the factors of 18. \(18 \div 1 = 18\) (1 row of 18 cars) \(18 \div 2 = 9\) (2 rows of 9 cars) \(18 \div 3 = 6\) (3 rows of 6 cars) \(18 \div 6 = 3\) (6 rows of 3 cars) \(18 \div 9 = 2\) (9 rows of 2 cars) \(18 \div 18 = 1\) (18 rows of 1 car) The factors are: 1, 2, 3, 6, 9, 18 Final Answer: 1, 2, 3, 6, 9, or 18 rows
Q18: Two buses leave the station at the same time. The first bus returns to the station every 15 minutes, and the second bus returns every 20 minutes. After how many minutes will both buses be at the station together again?
Solution:
Ans: We need to find the LCM of 15 and 20. Multiples of 15: 15, 30, 45, 60, 75... Multiples of 20: 20, 40, 60, 80... The LCM is 60. Final Answer: 60 minutes
Q19: A teacher has 30 pencils and 45 erasers to distribute equally among students. What is the greatest number of students who can receive supplies if each student gets the same number of pencils and the same number of erasers with none left over?
Solution:
Ans: We need to find the GCF of 30 and 45. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Factors of 45: 1, 3, 5, 9, 15, 45 The GCF is 15. Each student will get \(30 \div 15 = 2\) pencils and \(45 \div 15 = 3\) erasers. Final Answer: 15 students
Q20: Emma is making a pattern with tiles. She places square tiles in rows. If she has 28 tiles, how many different rectangular arrangements can she make? (Count each different rectangle as one arrangement.)
Solution:
Ans: We need to find all factor pairs of 28. \(1 \times 28 = 28\) (1 row and 28 columns or 28 rows and 1 column) \(2 \times 14 = 28\) (2 rows and 14 columns or 14 rows and 2 columns) \(4 \times 7 = 28\) (4 rows and 7 columns or 7 rows and 4 columns) There are 3 different pairs, giving us 6 different rectangular arrangements (since each pair creates 2 arrangements). Final Answer: 6 different rectangular arrangements
The document Worksheet (with Solutions): Factors and Multiples is a part of the Grade 4 Course Math Grade 4.
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