Integers, Factors & Multiples

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Integers, Factors & Multiples MCQ & Objective Questions

Understanding "Integers, Factors & Multiples" is crucial for students preparing for school and competitive exams. Mastering these concepts not only enhances mathematical skills but also boosts confidence during exams. Practicing MCQs and objective questions helps students identify important questions, ensuring effective exam preparation and improved scores.

What You Will Practise Here

  • Definition and properties of integers
  • Understanding factors and multiples, including prime factors
  • Finding the least common multiple (LCM) and greatest common divisor (GCD)
  • Applications of integers in real-life scenarios
  • Solving problems involving addition, subtraction, multiplication, and division of integers
  • Identifying and solving word problems related to factors and multiples
  • Practice with various objective questions and MCQs for better retention

Exam Relevance

The topic of "Integers, Factors & Multiples" is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to apply concepts in problem-solving scenarios. Common question patterns include identifying factors of a number, calculating LCM and GCD, and solving word problems that involve integers.

Common Mistakes Students Make

  • Confusing between factors and multiples, leading to incorrect answers
  • Overlooking negative integers when solving problems
  • Miscalculating LCM and GCD due to lack of practice
  • Failing to read word problems carefully, resulting in misunderstanding the question

FAQs

Question: What are integers?
Answer: Integers are whole numbers that can be positive, negative, or zero, without any fractional or decimal parts.

Question: How do I find the LCM of two numbers?
Answer: The LCM can be found by listing the multiples of each number and identifying the smallest common multiple, or by using the formula LCM(a, b) = (a * b) / GCD(a, b).

Start solving practice MCQs on "Integers, Factors & Multiples" today to enhance your understanding and ace your exams!

Q. How many factors does the number 28 have?
  • A. 4
  • B. 6
  • C. 8
  • D. 10
Q. How many factors does the number 36 have?
  • A. 6
  • B. 8
  • C. 9
  • D. 12
Q. How many integers between 1 and 100 are multiples of 5?
  • A. 20
  • B. 19
  • C. 21
  • D. 22
Q. How many multiples of 5 are there between 1 and 50?
  • A. 8
  • B. 9
  • C. 10
  • D. 11
Q. If a number is a multiple of 9 and less than 100, what is the largest such number?
  • A. 81
  • B. 90
  • C. 99
  • D. 72
Q. If a number is a multiple of both 3 and 5, what is the smallest number greater than 10?
  • A. 15
  • B. 20
  • C. 25
  • D. 30
Q. If a number is a multiple of both 5 and 7, what is the smallest such number?
  • A. 35
  • B. 70
  • C. 25
  • D. 50
Q. If a number is a multiple of both 5 and 9, what is the smallest such number?
  • A. 45
  • B. 90
  • C. 60
  • D. 75
Q. If a number is divisible by 9, which of the following must also be true?
  • A. It is divisible by 3
  • B. It is divisible by 6
  • C. It is divisible by 12
  • D. It is divisible by 18
Q. If a number is divisible by both 4 and 6, what is the least possible value of that number?
  • A. 12
  • B. 24
  • C. 36
  • D. 48
Q. If a number is divisible by both 4 and 6, what is the smallest positive integer that it can be?
  • A. 12
  • B. 24
  • C. 18
  • D. 30
Q. If a number is divisible by both 4 and 6, what is the smallest positive integer that is also a multiple of both?
  • A. 12
  • B. 24
  • C. 36
  • D. 48
Q. What is the greatest common divisor (GCD) of 48 and 64?
  • A. 8
  • B. 12
  • C. 16
  • D. 24
Q. What is the least common multiple (LCM) of 8 and 12?
  • A. 24
  • B. 48
  • C. 36
  • D. 60
Q. What is the product of all prime factors of 30?
  • A. 30
  • B. 60
  • C. 15
  • D. 45
Q. What is the sum of all factors of 12?
  • A. 28
  • B. 24
  • C. 36
  • D. 30
Q. What is the sum of all factors of 24?
  • A. 60
  • B. 70
  • C. 80
  • D. 90
Q. Which of the following is a multiple of 7?
  • A. 28
  • B. 30
  • C. 32
  • D. 34
Q. Which of the following is NOT a factor of 100?
  • A. 2
  • B. 4
  • C. 5
  • D. 10
Q. Which of the following is NOT a factor of 45?
  • A. 1
  • B. 3
  • C. 5
  • D. 7
Q. Which of the following numbers is a factor of 84?
  • A. 6
  • B. 10
  • C. 14
  • D. 20
Q. Which of the following numbers is a multiple of 7?
  • A. 28
  • B. 30
  • C. 32
  • D. 34
Q. Which of the following numbers is a multiple of 9?
  • A. 27
  • B. 28
  • C. 30
  • D. 31
Q. Which of the following numbers is NOT a factor of 100?
  • A. 4
  • B. 5
  • C. 10
  • D. 20
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