Greatest Common Factor of 35 and 140 by Prime Factorization

Given Numbers: 35, 140
Identify the Prime Factors of 35 and 140 by Prime Factorization

• Prime Factorization of 35: 35 = 5 x 7 = 5¹ x 7¹
• Prime Factorization of 140: 140 = 2 x 2 x 5 x 7 = 2² x 5¹ 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 35 and 140

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

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

As a result, the Greatest Common Factor (GCF) of 35 and 140 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(35, 140) = 5¹ x 7¹
• GCF(35, 140) = 5 x 7
• GCF(35, 140) = 35

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