Given Numbers: 35, 63
Identify the Prime Factors of 35 and 63 by Prime Factorization
Identify the Prime Factors of 35 and 63 by Prime Factorization
- Prime Factorization of 35: 35 = 5 x 7 = 51 x 71
- Prime Factorization of 63: 63 = 3 x 3 x 7 = 32 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 35 and 63
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 35 and 63 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 (35, 63) = 71
- GCF(35, 63) = 7
Therefore, the Greatest Common Factor of 35 and 63 by Prime Factorization = 7