how to find hcf and lcm using prime factorization methods
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First find the prime factors of thw numbers ;
Then group the same numbers by their powers
- Eg = 80
- 80 = 2×2×2×2×5
- 80 = 2⁴ × 5¹
Then for HCF ;
- find the same factor(s) out of all the numbers and only multiply thier highest powers.
Then for LCM ;
- find the highest power of all the factors and multiply them that many times.
Eg: 16 , 20
16 = 2×2×2×2 = 2⁴
20 = 2×2×5 = 2²×5¹
- Thus HCF = 2² = 4
- Thus LCM = 2⁴ × 5¹ = 16×5 = 80
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