Given Numbers: 15, 30, 45
Identify the Prime Factors of 15, 30 and 45 by Prime Factorization
Identify the Prime Factors of 15, 30 and 45 by Prime Factorization
- Prime Factorization of 15: 15 = 3 x 5 = 31 x 51
- Prime Factorization of 30: 30 = 2 x 3 x 5 = 21 x 31 x 51
- Prime Factorization of 45: 45 = 3 x 3 x 5 = 32 x 51
Determine the Prime Factor(s) that are common to the Prime Factorization of each number:
- 3 and 5 are Prime Factors common to the Prime Factorizations of 15, 30 and 45
Determine the least number of occurrences of 3 and 5 among the Prime Factorizations:
- 3 occurs at least 1 time in each Prime Factorization
- 5 occurs 1 time in each Prime Factorization
As a result, the Greatest Common Factor (GCF) of 15, 30 and 45 is equal to 3 x 5, which equals the product of 3 and 5 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:
- GCF(15, 30, 45) = 31 x 51
- GCF(15, 30, 45) = 3 x 5
- GCF(15, 30, 45) = 15
Therefore, the Greatest Common Factor of 15, 30 and 45 by Prime Factorization = 15