Greatest Common Factor of 19, 38, 57 and 95 by Prime Factorization

Given Numbers: 19, 38, 57, 95
Identify the Prime Factors of 19, 38, 57 and 95 by Prime Factorization

• Prime Factorization of 19: 19 = 19¹ (prime number)
• Prime Factorization of 38: 38 = 2 x 19 = 2¹ x 19¹
• Prime Factorization of 57: 57 = 3 x 19 = 3¹ x 19¹
• Prime Factorization of 95: 95 = 5 x 19 = 5¹ x 19¹

Determine the Prime Factor(s) that are common to the Prime Factorization of each number:

• 19 is the only Prime Factor common to the Prime Factorizations of 19, 38, 57 and 95

Determine the least number of occurrences of 19 among the Prime Factorizations:

• 19 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 19, 38, 57 and 95 is equal to 19, which equals 19 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (19, 38, 57, 95) = 19¹
• GCF(19, 38, 57, 95) = 19

Therefore, the Greatest Common Factor of 19, 38, 57 and 95 by Prime Factorization = 19