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Do larger numbers have more prime factors than smaller ones?
Last updated at January 22, 2026 by Teachoo
Prime Factorisation
Prime Factorisation
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Class 7 (Ganita Prakash 1, 2 & old NCERT)
Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)
- The Greatest of All
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Prime Factorisation
- Finding HCF using Prime Factorisation
- Figure it out - Page 54
- Least, but not Last!
- Finding LCM using Prime Factorisation
- Patterns, Properties, and a Pretty Procedure!
- Figure it out - Page 59
- Miscellenaous Questions on HCF, LCM
- Efficient Procedures for HCF and LCM
- Property Involving both the HCF and the LCM
- Figure it out - Page 63, 64
Transcript
Do larger numbers have more prime factors than smaller ones?No, they do not Explanation: The length of a prime factorisation depends on how small the prime factors are, not just how big the total number is. If a number is built from tiny bricks (like 2s), you need a LOT of them, so the chain is long. If a number is built from huge bricks (like 11s, 13s, or bigger), you only need a few, so the chain is short. Examples 96 (Smaller number) →2 × 2 × 2 × 2 × 2 × 3 (Length: 6 factors) 𝟏𝟐𝟏 (Larger number) →11×11 (Length: 𝟐 factors) More examples 64: 2 × 2 × 2 × 2 × 2 × 2 (Length: 6 ) 169: 13 × 13 (Length: 2 ) Even though 169 is much bigger than 64, its prime factorisation is much shorter because the "bricks" (13) are bigger.
