Greatest Common Factor of 140 and 175 by Prime Factorization

Given Numbers: 140, 175
Identify the Prime Factors of 140 and 175 by Prime Factorization

• Prime Factorization of 140: 140 = 2 x 2 x 5 x 7 = 2² x 5¹ x 7¹
• Prime Factorization of 175: 175 = 5 x 5 x 7 = 5² x 7¹

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

• 5 and 7 are Prime Factors common to the Prime Factorizations of 140 and 175

Determine the least number of occurrences of 5 and 7 among the Prime Factorizations:

• 5 occurs at least 1 time in each Prime Factorization
• 7 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 140 and 175 is equal to 5 x 7, which equals the product of 5 and 7 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(140, 175) = 5¹ x 7¹
• GCF(140, 175) = 5 x 7
• GCF(140, 175) = 35

Therefore, the Greatest Common Factor of 140 and 175 by Prime Factorization = 35