Given Numbers: 12, 24
Identify the Prime Factors of 12 and 24 by Prime Factorization
Identify the Prime Factors of 12 and 24 by Prime Factorization
- Prime Factorization of 12: 12 = 2 x 2 x 3 = 22 x 31
- Prime Factorization of 24: 24 = 2 x 2 x 2 x 3 = 23 x 31
Determine the Prime Factor(s) that are common to the Prime Factorization of each number:
- 2 and 3 are Prime Factors common to the Prime Factorizations of 12 and 24
Determine the least number of occurrences of 2 and 3 among the Prime Factorizations:
- 2 occurs at least 2 times in each Prime Factorization
- 3 occurs 1 time in each Prime Factorization
As a result, the Greatest Common Factor (GCF) of 12 and 24 is equal to 2 x 2 x 3, which equals the product of 2 and 3 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:
- GCF(12, 24) = 22 x 31 = 2 x 2 x 3
- GCF(12, 24) = 4 x 3
- GCF(12, 24) = 12
Therefore, the Greatest Common Factor of 12 and 24 by Prime Factorization = 12