Given Numbers: 6, 9, 15
Identify the Prime Factors of 6, 9 and 15 by Prime Factorization
Identify the Prime Factors of 6, 9 and 15 by Prime Factorization
- Prime Factorization of 6: 6 = 2 x 3 = 21 x 31
- Prime Factorization of 9: 9 = 3 x 3 = 32
- Prime Factorization of 15: 15 = 3 x 5 = 31 x 51
Determine the Prime Factor(s) that are common to the Prime Factorization of each number:
- 3 is the only Prime Factor common to the Prime Factorizations of 6, 9 and 15
Determine the least number of occurrences of 3 among the Prime Factorizations:
- 3 occurs at least 1 time in each Prime Factorization
As a result, the Greatest Common Factor (GCF) of 6, 9 and 15 is equal to 3, which equals 3 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:
- GCF (6, 9, 15) = 31
- GCF(6, 9, 15) = 3
Therefore, the Greatest Common Factor of 6, 9 and 15 by Prime Factorization = 3