Prime factorization is the process of expressing a number as a product of prime numbers. For example, 24 = 2³ × 3. It breaks down the number into its smallest divisible prime components. 75 is not divisible by 21. The prime factorization of 75 is 3 × 5², and 21 is 3 × 7. Since 7 is not a factor of 75, divisibility fails.
Class 6 Mathematics Chapter 5 Prime Time question answer
Class 6 NCERT Ganita Prakash Chapter 5 Prime Time
To determine divisibility, use prime factorizations:
• 75 = 3 × 5²
• 21 = 3 × 7
While both share the factor 3, 75 lacks the factor 7, which is required for divisibility. As a result, the prime factorization of 21 is not fully included in that of 75. Dividing confirms this: 75 ÷ 21 leaves a remainder, proving that 75 is not divisible by 21.
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