Question
What is the greatest common factor of 14,28,42?
a
14
b
7
c
2
a
14
b
7
c
2
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the numbers 14, 28, and 42, we can first determine the prime factorization of each number:
- **14**: \(2 \times 7\)
- **28**: \(2^2 \times 7\)
- **42**: \(2 \times 3 \times 7\)
Next, we identify the common factors among all three numbers, which are:
- **2** from \(2\)
- **7** from \(7\)
To find the GCF, we take the lowest power of each common prime factor:
- The factor **2** appears in all three numbers as \(2^1\).
- The factor **7** appears in all three numbers as \(7^1\).
Now, we multiply these together:
\[
GCF = 2^1 \times 7^1 = 2 \times 7 = 14
\]
Thus, the greatest common factor of the numbers 14, 28, and 42 is \(14\).
The correct answer is:
**a 14**
- **14**: \(2 \times 7\)
- **28**: \(2^2 \times 7\)
- **42**: \(2 \times 3 \times 7\)
Next, we identify the common factors among all three numbers, which are:
- **2** from \(2\)
- **7** from \(7\)
To find the GCF, we take the lowest power of each common prime factor:
- The factor **2** appears in all three numbers as \(2^1\).
- The factor **7** appears in all three numbers as \(7^1\).
Now, we multiply these together:
\[
GCF = 2^1 \times 7^1 = 2 \times 7 = 14
\]
Thus, the greatest common factor of the numbers 14, 28, and 42 is \(14\).
The correct answer is:
**a 14**