NCERT Solutions Class 6 Maths Chapter 7 — Prime Numbers & Factorization

Solution:

Step 1: Factors are numbers that divide a given number exactly, leaving no remainder.

Step 2: Every number can be divided by 1. For example, 5 ÷ 1 = 5, 100 ÷ 1 = 100.

Step 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.

Solution:

Step 1: A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.

Step 2: For 9, the factors are 1, 3, 9 (more than two factors). So, 9 is composite.

Step 3: For 15, the factors are 1, 3, 5, 15 (more than two factors). So, 15 is composite.

Step 4: For 21, the factors are 1, 3, 7, 21 (more than two factors). So, 21 is composite.

Step 5: For 13, the factors are 1, 13 (exactly two factors). Thus, 13 is a prime number.

Solution:

Step 1: A composite number is a natural number greater than 1 that has more than two factors.

Step 2: Number 2 has factors 1, 2 (prime).

Step 3: Number 3 has factors 1, 3 (prime).

Step 4: Number 4 has factors 1, 2, 4 (more than two factors), so it is a composite number.

Step 5: Number 5 has factors 1, 5 (prime).

Solution:

Step 1: Prime factorization is the process of expressing a composite number as a product of its prime factors.

Step 2: First, check if all factors in Ravi's expression (2, 3, 5) are prime numbers. Yes, they are.

Step 3: Next, check if their product equals the original number: 2 × 3 × 5 = 6 × 5 = 30. Yes, it does.

Step 4: Therefore, Ravi's prime factorization is correct. 1 is not included in prime factorization, and the order of factors does not matter.

Solution:

Step 1: A prime number has exactly two distinct factors: 1 and itself. The number 1 has only one factor (1 itself).

Step 2: A composite number has more than two factors. The number 1 has only one factor.

Step 3: Since 1 does not fit either definition, it is classified as neither a prime nor a composite number.