Find the GCF of 35, 56, and 63.
i need help to
35 = 5*7
56 = 8*7
63 = 9*7
So, what do you think? Which factor is common to all?
To find the greatest common factor (GCF) of 35, 56, and 63, you can use prime factorization method or the method of finding common factors.
1. Prime Factorization Method:
Step 1: Find the prime factors of each number.
- The prime factorization of 35 is 5 x 7.
- The prime factorization of 56 is 2 x 2 x 2 x 7.
- The prime factorization of 63 is 3 x 3 x 7.
Step 2: Determine the common prime factors.
- The common prime factors among the three numbers are 7.
Step 3: Multiply the common prime factors.
7
So, the GCF of 35, 56, and 63 is 7.
2. Method of Finding Common Factors:
Step 1: List the factors of each number.
- The factors of 35 are 1, 5, 7, and 35.
- The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
- The factors of 63 are 1, 3, 7, 9, 21, and 63.
Step 2: Determine the common factors.
- The common factors among the three numbers are 1 and 7.
Step 3: Find the largest common factor.
7
Therefore, the GCF of 35, 56, and 63 is 7.