Prime Time | Class 6 Mathematics Notes

Prime Factorization

This section introduces prime factorization, the process of expressing a composite number as a product of prime numbers. It explains that every composite number can be broken down uniquely into prime factors, which is known as the Fundamental Theorem of Arithmetic. The method involves dividing the composite number by the smallest possible prime number repeatedly until the quotient becomes 1. The prime numbers used in the division are the prime factors. For example, the prime factorization of 24 is 2 × 2 × 2 × 3 or 2³ × 3. The section provides step-by-step examples and emphasizes the uniqueness of prime factorization for each number. It also discusses the use of factor trees and division methods to find prime factors. Understanding prime factorization is essential for finding HCF and LCM, simplifying fractions, and solving problems involving divisibility.

📊 Diagram: Table on page 4 (3×10) shows numbers 31 to 70 to help identify primes and composites for factorization practice.

🧪 Activity: Students perform prime factorization of given composite numbers using division and factor trees.

🔗 Connection: This section leads to the 'Highest Common Factor (HCF)' section, where prime factorization is used to find common factors.

Table on page 4 (3×10)

Table on page 20 (1×2)

Table on page 21 (4×4)

Table on page 21 (4×4)

Table on page 21 (1×2)

Table on page 21 (1×2)

Table on page 21 (1×2)

Table on page 21 (1×2)

Table on page 21 (3×4)

Table on page 21 (3×4)

Table on page 22 (4×4)

Table on page 22 (4×4)

Table on page 33 (1×4)

| Numbers | a) Remainder when divided by 10 | b) Remainder when divided by 5 | c) Remainder when divided by 2 |

| 78 99 173 572 980 1111 2345 | 8 9 3 2 0 1 5 | 3 4 3 2 0 1 0 | 0 1 1 0 0 1 1 |