GCF(12, 30, 210)
To find the greatest common factor (GCF) of 12, 30, and 210, we need to find the largest number that divides evenly into all three numbers.
First, let's find the prime factorization of each number:
12 = 2^2 * 3
30 = 2 * 3 * 5
210 = 2 * 3 * 5 * 7
Next, let's find the common factors among these prime factorizations:
The highest power of 2 among the prime factorizations is 2^1.
The highest power of 3 among the prime factorizations is 3^1.
The highest power of 5 among the prime factorizations is 5^1.
There is no common factor of 7 in the prime factorizations.
Therefore, the GCF of 12, 30, and 210 is 2^1 * 3^1 * 5^1 = 2 * 3 * 5 = 30.
To find the greatest common factor (GCF) of 12, 30, and 210, you can follow these steps:
Step 1: Find the prime factors of each number.
- Prime factors of 12: 2 × 2 × 3 = 2² × 3
- Prime factors of 30: 2 × 3 × 5 = 2 × 3 × 5
- Prime factors of 210: 2 × 3 × 5 × 7 = 2 × 3 × 5 × 7
Step 2: Identify the common prime factors among the three numbers.
- The common prime factors are 2 and 3.
Step 3: Find the smallest exponent for each common prime factor.
- For the common factor 2, the smallest exponent is 1.
- For the common factor 3, the smallest exponent is 1.
Step 4: Multiply the common prime factors raised to their smallest exponents.
- GCF = 2^1 × 3^1 = 2 × 3 = 6
Therefore, the GCF of 12, 30, and 210 is 6.
To find the Greatest Common Factor (GCF) of 12, 30, and 210, we can start by finding the common factors of these numbers.
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
The factors of 210 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
Now, let's find the common factors among these three numbers:
The common factors of 12, 30, and 210 are 1, 2, 3, 6.
Therefore, the Greatest Common Factor (GCF) of 12, 30, and 210 is 6.