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Factors & Multiples

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Q. If a number is divisible by both 4 and 6, which of the following must also be true? (2023)
  • A. It is divisible by 12.
  • B. It is divisible by 24.
  • C. It is divisible by 10.
  • D. It is not divisible by 2.
Q. If a number is divisible by both 5 and 10, which of the following can be concluded?
  • A. It is a multiple of 15.
  • B. It is a multiple of 20.
  • C. It is a multiple of 50.
  • D. It is a multiple of 10.
Q. If a number is divisible by both 6 and 8, which of the following must it also be divisible by?
  • A. 12
  • B. 24
  • C. 18
  • D. 36
Q. If a number is divisible by both 8 and 12, what is the smallest number it could be?
  • A. 24
  • B. 48
  • C. 96
  • D. 72
Q. If a number is divisible by both 8 and 12, which of the following must also be true?
  • A. It is divisible by 24.
  • B. It is divisible by 16.
  • C. It is divisible by 20.
  • D. It is divisible by 32.
Q. If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
  • A. 16
  • B. 24
  • C. 20
  • D. 36
Q. If a number is divisible by both 9 and 12, which of the following is guaranteed to be true?
  • A. It is divisible by 36.
  • B. It is divisible by 108.
  • C. It is divisible by 27.
  • D. It is divisible by 18.
Q. If the GCD of two numbers is 1, what can be inferred about the two numbers? (2023)
  • A. They are both even.
  • B. They are both odd.
  • C. They are coprime.
  • D. They are multiples of each other.
Q. If the GCD of two numbers is 1, which of the following statements is true?
  • A. The numbers are multiples of each other
  • B. The numbers are co-prime
  • C. The numbers are both even
  • D. The numbers are both odd
Q. If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?
  • A. It is 216.
  • B. It is 72.
  • C. It is 36.
  • D. It is 6.
Q. If the least common multiple (LCM) of two numbers is 60 and one of the numbers is 15, what could be the other number?
  • A. 20
  • B. 30
  • C. 45
  • D. 60
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what can be inferred about the product of the two numbers?
  • A. It is 720.
  • B. It is 60.
  • C. It is 12.
  • D. It is 5.
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?
  • A. (5, 12)
  • B. (10, 30)
  • C. (15, 20)
  • D. (5, 15)
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
  • A. 720
  • B. 180
  • C. 120
  • D. 60
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, what is the product of the two numbers?
  • A. 300
  • B. 60
  • C. 12
  • D. 15
Q. If the number 36 is expressed in terms of its prime factors, which of the following is correct?
  • A. 2^2 * 3^2
  • B. 2^3 * 3^1
  • C. 3^2 * 4^1
  • D. 6^2
Q. If the product of two consecutive integers is 72, which of the following pairs could represent those integers?
  • A. 8 and 9
  • B. 6 and 7
  • C. 5 and 6
  • D. 4 and 5
Q. If the product of two consecutive integers is 72, which of the following pairs could represent these integers?
  • A. 8 and 9
  • B. 6 and 7
  • C. 5 and 6
  • D. 9 and 10
Q. If the product of two numbers is 144 and one of the numbers is 12, what is the other number? (2023)
  • A. 12
  • B. 10
  • C. 8
  • D. 6
Q. If the product of two numbers is 48 and one of the numbers is 6, what can be inferred about the other number?
  • A. It is 8.
  • B. It is 12.
  • C. It is 6.
  • D. It is 4.
Q. If the product of two numbers is 48, which of the following pairs could represent these numbers?
  • A. (2, 24)
  • B. (3, 16)
  • C. (4, 12)
  • D. (All of the above)
Q. If the product of two numbers is 72 and one of the numbers is 8, what is the other number?
  • A. 6
  • B. 9
  • C. 10
  • D. 12
Q. If the product of two numbers is a multiple of 15, which of the following must be true?
  • A. At least one of the numbers is a multiple of 3.
  • B. At least one of the numbers is a multiple of 5.
  • C. Both numbers are even.
  • D. Both numbers are odd.
Q. If the sum of the factors of a number is 28, which of the following could be the number?
  • A. 12
  • B. 18
  • C. 20
  • D. 24
Q. If the sum of two multiples of 7 is 56, which of the following pairs could represent these multiples?
  • A. 21 and 35
  • B. 14 and 42
  • C. 28 and 28
  • D. All of the above.
Q. If the sum of two numbers is 30 and one of the numbers is a multiple of 5, which of the following could be the other number?
  • A. 10
  • B. 15
  • C. 20
  • D. 25
Q. If the sum of two numbers is 30 and one of them is a multiple of 5, which of the following could be the two numbers?
  • A. 10 and 20
  • B. 15 and 15
  • C. 5 and 25
  • D. 12 and 18
Q. If the sum of two numbers is 30 and one of them is a multiple of 5, which of the following pairs could represent these numbers?
  • A. 10 and 20
  • B. 15 and 15
  • C. 5 and 25
  • D. 12 and 18
Q. If the sum of two numbers is 30 and one of them is a multiple of 6, which of the following could be the two numbers?
  • A. 12 and 18
  • B. 10 and 20
  • C. 6 and 24
  • D. 15 and 15
Q. If the sum of two numbers is a multiple of 10, which of the following can be inferred?
  • A. Both numbers are even.
  • B. Both numbers are odd.
  • C. At least one number is even.
  • D. At least one number is odd.
Showing 31 to 60 of 122 (5 Pages)

Factors & Multiples MCQ & Objective Questions

Understanding "Factors & Multiples" is crucial for students preparing for various exams in India. This topic forms the foundation for many mathematical concepts and is frequently tested in objective questions. Practicing MCQs related to factors and multiples not only enhances conceptual clarity but also boosts your confidence in tackling important questions during exams.

What You Will Practise Here

  • Definition and identification of factors and multiples
  • Prime factors and their significance
  • Finding the least common multiple (LCM) and greatest common divisor (GCD)
  • Applications of factors and multiples in problem-solving
  • Word problems involving factors and multiples
  • Common patterns and tricks for quick calculations
  • Practice questions with detailed explanations and answers

Exam Relevance

The topic of factors and multiples is a staple in CBSE and State Board examinations, as well as competitive exams like NEET and JEE. Questions often include finding LCM and GCD, identifying factors of given numbers, and solving real-world problems. Familiarity with this topic can significantly improve your performance, as it frequently appears in both objective and subjective formats.

Common Mistakes Students Make

  • Confusing factors with multiples, leading to incorrect answers
  • Overlooking the importance of prime factorization in solving problems
  • Miscalculating LCM and GCD due to lack of practice
  • Ignoring word problems that require a clear understanding of the concepts

FAQs

Question: What are factors and multiples?
Answer: Factors are numbers that divide another number exactly, while multiples are the result of multiplying a number by an integer.

Question: How can I find the LCM of two numbers?
Answer: The LCM can be found using the prime factorization method or by listing the multiples of the numbers until you find the smallest common one.

Start your journey towards mastering factors and multiples today! Solve practice MCQs to test your understanding and improve your exam readiness. Remember, consistent practice is the key to success!

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