Find the greatest common factor of 27 and 54(1 point) Responses
1. 9
2. 3
3. 6
4. 27
The greatest common factor of 27 and 54 is 27. So the correct response is (4) 27.
To find the greatest common factor (GCF) of 27 and 54, we need to list the factors of both numbers and find the largest number that appears in both lists.
The factors of 27 are: 1, 3, 9, and 27.
The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54.
The largest number that appears in both lists is 9. Therefore, the GCF of 27 and 54 is 9.
So, the correct answer is option 1: 9.
To find the greatest common factor (GCF) of 27 and 54, you can start by finding the prime factorization of each number.
To find the prime factorization of 27, you can divide it by prime numbers starting with 2. However, 27 is not divisible by 2. So you move on to the next prime number, which is 3. Divide 27 by 3, and you get 9. Since 9 is also divisible by 3, divide it by 3 again to get 3. Therefore, the prime factorization of 27 is 3 x 3 x 3, which can be written as 3^3.
To find the prime factorization of 54, follow the same process. Start with 2, but 54 is not divisible by 2 either. Move on to 3, and you'll find that 54 is divisible by 3. Divide 54 by 3, and you get 18. Again, divide 18 by 3, and you get 6. So the prime factorization of 54 is 2 x 3 x 3 x 3, which can be written as 2 x 3^3.
Now that we have the prime factorizations of 27 and 54, we can find their GCF by multiplying the common factors once. In this case, the only common factor is 3 raised to the power of 1, which is 3. Therefore, the greatest common factor of 27 and 54 is 3.
So the correct response is option 2: 3.