Given Numbers: 50, 75, 100
Identify the Prime Factors of 50, 75 and 100 by Prime Factorization
Identify the Prime Factors of 50, 75 and 100 by Prime Factorization
- Prime Factorization of 50: 50 = 2 x 5 x 5 = 21 x 52
- Prime Factorization of 75: 75 = 3 x 5 x 5 = 31 x 52
- Prime Factorization of 100: 100 = 2 x 2 x 5 x 5 = 22 x 52
Determine the Prime Factor(s) that are common to the Prime Factorization of each number:
- 5 is the only Prime Factor common to the Prime Factorizations of 50, 75 and 100
Determine the least number of occurrences of 5 among the Prime Factorizations:
- 5 occurs 2 times in each Prime Factorization
As a result, the Greatest Common Factor (GCF) of 50, 75 and 100 is equal to 5 x 5, which equals 5 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:
- GCF(50, 75, 100) = 52 = 5 x 5
- GCF(50, 75, 100) = 25
Therefore, the Greatest Common Factor of 50, 75 and 100 by Prime Factorization = 25