What is the greatest common factor of 6, 9 and 15
The Correct Answer and Explanation is:
Correct Answer:
The greatest common factor (GCF) of 6, 9, and 15 is 3.
Explanation:
The greatest common factor is the largest number that divides exactly into two or more numbers. To find the GCF of 6, 9, and 15, we follow these steps:
Step 1: Find the factors of each number.
- Factors of 6: 1, 2, 3, 6
- Factors of 9: 1, 3, 9
- Factors of 15: 1, 3, 5, 15
Step 2: Identify the common factors.
Looking at all the factors, we see that 1 and 3 appear in all three lists. So, the common factors of 6, 9, and 15 are 1 and 3.
Step 3: Choose the greatest one.
Out of the common factors, the greatest one is 3.
Therefore, the greatest common factor of 6, 9, and 15 is 3.
This means that 3 is the largest number that can divide 6, 9, and 15 without leaving a remainder. Knowing how to find the GCF is useful when simplifying fractions, solving problems involving ratios, or factoring expressions in algebra.
Alternatively, we can use the prime factorization method:
- 6 = 2 × 3
- 9 = 3 × 3
- 15 = 3 × 5
Each number has a factor of 3. That is the only prime factor they all have in common.
Understanding how to find the GCF improves your number sense and problem-solving ability. It is especially important in reducing fractions to their simplest form or when working with least common multiples. It also appears in many real-life situations such as dividing items equally, making groups, or adjusting recipes. The GCF represents the largest group size that can be made with equal sharing.
