Given Numbers: 35, 49, 56
Identify the Prime Factors of 35, 49 and 56 by Prime Factorization
Identify the Prime Factors of 35, 49 and 56 by Prime Factorization
- Prime Factorization of 35: 35 = 5 x 7 = 51 x 71
- Prime Factorization of 49: 49 = 7 x 7 = 72
- Prime Factorization of 56: 56 = 2 x 2 x 2 x 7 = 23 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, 49 and 56
Determine the least number of occurrences of 7 among the Prime Factorizations:
- 7 occurs at least 1 time in each Prime Factorization
As a result, the Greatest Common Factor (GCF) of 35, 49 and 56 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, 49, 56) = 71
- GCF(35, 49, 56) = 7
Therefore, the Greatest Common Factor of 35, 49 and 56 by Prime Factorization = 7