What is the greatest common factor of 6, 14, and 30
The Correct Answer and Explanation is:
To find the greatest common factor (GCF) of 6, 14, and 30, we start by identifying the factors of each number.
Step 1: List the factors of each number
- Factors of 6: 1, 2, 3, 6
- Factors of 14: 1, 2, 7, 14
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Step 2: Identify the common factors
The numbers 6, 14, and 30 all have the following common factors:
- 1
- 2
So the greatest of the common factors is 2.
Final Answer: 2
Explanation
The greatest common factor, or GCF, is the largest positive number that divides evenly into each of the numbers in a given set. In this case, we are finding the GCF of 6, 14, and 30. The process starts by determining all the factors for each of the three numbers.
A factor is a whole number that divides another number exactly, leaving no remainder. For example, 2 is a factor of 6 because 6 divided by 2 equals 3 with no remainder. Similarly, 2 is a factor of both 14 and 30.
Listing all factors helps make it easy to see which ones they have in common. For 6, the factors are 1, 2, 3, and 6. For 14, they are 1, 2, 7, and 14. For 30, the factors include 1, 2, 3, 5, 6, 10, 15, and 30. Comparing these lists, we see that the only numbers common to all three lists are 1 and 2. Among these, the greatest value is 2.
There is another way to approach the problem by using prime factorization. The prime factorization of 6 is 2 times 3. For 14, it is 2 times 7. For 30, it is 2 times 3 times 5. The only prime number that appears in all three factorizations is 2. Therefore, the GCF is again 2.
Finding the GCF is useful in simplifying fractions, solving problems involving ratios, and understanding the relationships among numbers. In this example, since 2 is the highest number that divides evenly into all three, it is the greatest common factor of 6, 14, and 30.
