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About Prime Numbers & Factorization — Class 6 CBSE

Identify primes and composites; find factors, multiples, HCF, and LCM using prime factorization. This topic is part of the CBSE Class 6 mathematics syllabus (chapter: Chapter 5). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Prime Numbers & Factorization

  • Understanding Factors and Multiples
  • Discovering Prime and Composite Numbers
  • Mastering Prime Factorization
  • Finding HCF using Prime Factorization
  • Finding LCM using Prime Factorization

Interactive lesson · about 15 minutes · checkpoint question after every unit

Prime Numbers & Factorization — solved examples for Class 6 CBSE

Example 1easy

Which of the following statements about factors is TRUE?
  1. A)A) Every number has exactly two factors.
  2. B)B) A factor of a number is always greater than or equal to the number itself.
  3. C)C) 1 is a factor of every number.
  4. D)D) The number of factors of a prime number is more than two.

Step-by-step solution

  1. Factors are numbers that divide a given number exactly, leaving no remainder.
  2. Every number can be divided by 1. For example, 5 ÷ 1 = 5, 100 ÷ 1 = 100.
  3. Therefore, 1 is a factor of every number. Options A, B, and D are incorrect based on the definitions of factors and prime numbers.

Answer: C) 1 is a factor of every number.

Example 2medium

Which of the following statements about numbers is INCORRECT?
  1. A)The number 1 is neither prime nor composite.
  2. B)Every prime number has exactly two factors.
  3. C)The smallest composite number is 4.
  4. D)All prime numbers are odd.

Step-by-step solution

  1. Statement A is correct: The number 1 has only one factor (itself), so it doesn't fit the definition of prime (exactly two factors) or composite (more than two factors).
  2. Statement B is correct: By definition, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
  3. Statement C is correct: The first few composite numbers are 4, 6, 8, 9, 10, ... The smallest among them is 4.
  4. Statement D is incorrect: The number 2 is a prime number, and it is an even number. It is the only even prime number.

Answer: All prime numbers are odd.

Example 3hard

A natural number 'N' has an odd number of factors. Which of the following statements must be true about N?
  1. A)N is a prime number
  2. B)N is a composite number
  3. C)N is a perfect square
  4. D)N is an even number

Step-by-step solution

  1. Factors of a number usually appear in pairs. For example, the factors of 12 are (1, 12), (2, 6), (3, 4).
  2. If a number has an odd number of factors, it means one of its factor pairs consists of the same number multiplied by itself. This happens only when the number is a perfect square.
  3. For example, 9 has factors 1, 3, 9 (3 factors, which is an odd number), and 9 is a perfect square (3 × 3).
  4. Therefore, any number with an odd number of factors must be a perfect square.

Answer: N is a perfect square

Practice questions on Prime Numbers & Factorization

  1. Q1.easy

    Which of the following numbers is a prime number?
    1. A)A) 9
    2. B)B) 15
    3. C)C) 21
    4. D)D) 13
    Show answer

    Answer: D) 13

    Hint: Remember the definition of a prime number: it has exactly two factors, 1 and the number itself.

  2. Q2.easy

    Which of the following numbers is a composite number?
    1. A)A) 2
    2. B)B) 3
    3. C)C) 4
    4. D)D) 5
    Show answer

    Answer: C) 4

    Hint: A composite number is a natural number greater than 1 that is not prime. It has more than two factors.

  3. Q3.easy

    Ravi tried to find the prime factorization of 30. He wrote: 30 = 2 × 3 × 5. Is Ravi's factorization correct?
    1. A)A) Yes, because 2, 3, and 5 are all prime numbers and their product is 30.
    2. B)B) No, because he forgot to include 1 in the factorization.
    3. C)C) No, because 30 is an even number, so it must only have 2 as a prime factor.
    4. D)D) No, because the order of prime factors should be from largest to smallest.
    Show answer

    Answer: A) Yes, because 2, 3, and 5 are all prime numbers and their product is 30.

    Hint: Remember the definition of prime factorization: expressing a number as a product of its prime factors.

  4. Q4.medium

    What is the sum of all factors of 28?
    1. A)28
    2. B)42
    3. C)56
    4. D)63
    Show answer

    Answer: 56

    Hint: First, list all the numbers that divide 28 completely. Then, add them up.

  5. Q5.medium

    How many numbers between 50 and 100 (excluding 50 and 100) are multiples of 7?
    1. A)6
    2. B)7
    3. C)8
    4. D)9
    Show answer

    Answer: 7

    Hint: Find the first multiple of 7 greater than 50 and the last multiple of 7 less than 100. Then, count them.

  6. Q6.medium

    Rohan claims that all odd numbers are prime numbers. Which of the following numbers can be used to prove Rohan wrong?
    1. A)7
    2. B)11
    3. C)13
    4. D)15
    Show answer

    Answer: 15

    Hint: To prove Rohan wrong, you need to find an odd number that is NOT prime. A non-prime number has more than two factors.

  7. Q7.hard

    The sum of two distinct prime numbers is 61. What is the product of these two prime numbers?
    1. A)118
    2. B)122
    3. C)120
    4. D)124
    Show answer

    Answer: 118

    Hint: Remember that 61 is an odd number. How can two numbers add up to an odd number? Consider the unique property of the prime number 2.

  8. Q8.hard

    A 4-digit number 7A8B is divisible by both 4 and 9. If A and B are distinct digits (0-9), what is the largest possible value of A+B?
    1. A)10
    2. B)12
    3. C)14
    4. D)16
    Show answer

    Answer: 12

    Hint: First, use the divisibility rule for 4 to find possible values for B. Then, apply the divisibility rule for 9 to find A, remembering that A and B must be different digits.

  9. Q9.hard

    A natural number N has exactly 6 factors. Its prime factorization is of the form p^a × q^b, where p and q are distinct prime numbers and a, b are positive integers. What is the smallest possible value of N?
    1. A)12
    2. B)18
    3. C)20
    4. D)24
    Show answer

    Answer: 12

    Hint: Recall the formula for the number of factors from prime factorization: if N = p^a × q^b, the number of factors is (a+1)(b+1). To minimize N, use the smallest prime numbers as bases.

These are 9 of the 60 questions available for Prime Numbers & Factorization. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.