Greatest Common Factor of 63, 77, 91 and 105 by Prime Factorization

Given Numbers: 63, 77, 91, 105
Identify the Prime Factors of 63, 77, 91 and 105 by Prime Factorization

• Prime Factorization of 63: 63 = 3 x 3 x 7 = 3² x 7¹
• Prime Factorization of 77: 77 = 7 x 11 = 7¹ x 11¹
• Prime Factorization of 91: 91 = 7 x 13 = 7¹ x 13¹
• Prime Factorization of 105: 105 = 3 x 5 x 7 = 3¹ x 5¹ x 7¹

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

• 7 is the only Prime Factor common to the Prime Factorizations of 63, 77, 91 and 105

Determine the least number of occurrences of 7 among the Prime Factorizations:

• 7 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 63, 77, 91 and 105 is equal to 7, which equals 7 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (63, 77, 91, 105) = 7¹
• GCF(63, 77, 91, 105) = 7

Therefore, the Greatest Common Factor of 63, 77, 91 and 105 by Prime Factorization = 7