Step-by-step explanation:
1. Prime Factorize each number:
o 108 = 2 x 2 x 3 x 3 (prime factors are 2, 3)
o 120 = 2 x 2 x 2 x 3 x 5 (prime factors are 2, 3, 5)
o 252 = 2 x 2 x 3 x 7 (prime factors are 2, 3, 7)
2. Identify common prime factors:
o All three numbers share the prime factors 2 and 3.
3. Find the HCF:
o The HCF is the product of the common prime factors raised to the lowest power in which they appear in each number.
o HCF = 2^2 (since 2 appears twice in all numbers) * 3^1 (since 3 appears only once in all numbers)
o HCF = 4 * 3 = 12
Therefore, the HCF of 108, 120, and 252 using prime factorization is 12.
