Given Numbers: 12, 18, 30, 32
Identify the Prime Factors of 12, 18, 30 and 32 by Prime Factorization
Identify the Prime Factors of 12, 18, 30 and 32 by Prime Factorization
- Prime Factorization of 12: 12 = 2 x 2 x 3 = 22 x 31
- Prime Factorization of 18: 18 = 2 x 3 x 3 = 21 x 32
- Prime Factorization of 30: 30 = 2 x 3 x 5 = 21 x 31 x 51
- Prime Factorization of 32: 32 = 2 x 2 x 2 x 2 x 2 = 25
Determine the Prime Factor(s) that are common to the Prime Factorization of each number:
- 2 is the only Prime Factor common to the Prime Factorizations of 12, 18, 30 and 32
Determine the least number of occurrences of 2 among the Prime Factorizations:
- 2 occurs at least 1 time in each Prime Factorization
As a result, the Greatest Common Factor (GCF) of 12, 18, 30 and 32 is equal to 2, which equals 2 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:
- GCF (12, 18, 30, 32) = 21
- GCF(12, 18, 30, 32) = 2
Therefore, the Greatest Common Factor of 12, 18, 30 and 32 by Prime Factorization = 2