Find the greatest common factor of the following numbers:
A. 27,45 and 63
B. 54,108 and 162
A. To find the greatest common factor of 27, 45, and 63, we can find the prime factorization of each number and then determine the factors they all have in common.
- The prime factorization of 27 is 3^3.
- The prime factorization of 45 is 3^2 × 5.
- The prime factorization of 63 is 3^2 × 7.
The common factors of 27, 45, and 63 are 3^2 and the greatest common factor is 3^2 = 9.
B. To find the greatest common factor of 54, 108, and 162, we can again find the prime factorization of each number and determine the common factors.
- The prime factorization of 54 is 2 × 3^3.
- The prime factorization of 108 is 2^2 × 3^3.
- The prime factorization of 162 is 2 × 3^4.
The common factors of 54, 108, and 162 are 2 × 3^3 and the greatest common factor is 2 × 3^3 = 54.