What is GCF of 30 and 42 ?

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 30 and 42, we can use a couple of methods, including prime factorization and listing the factors. Let’s go through both methods step by step.

Method 1: Prime Factorization

First, we need to break down each number into its prime factors.

Finding Prime Factors

• 30: The prime factors of 30 are 2, 3, and 5. We can express this as:
• 30 = 2 × 3 × 5
• 42: The prime factors of 42 are 2, 3, and 7. This can be written as:
• 42 = 2 × 3 × 7

Identifying Common Factors

Now, let’s identify the common prime factors between the two numbers:

• Both 30 and 42 share the prime factors 2 and 3.

Calculating the GCF

To find the GCF, we multiply the common prime factors:

• GCF = 2 × 3 = 6

Method 2: Listing Factors

Another way to find the GCF is by listing all the factors of each number and identifying the largest one they have in common.

Factors of Each Number

• Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

Finding the Common Factors

Now, let’s look for the common factors:

• Common factors: 1, 2, 3, 6

Determining the GCF

The largest of these common factors is:

• GCF = 6

Final Thoughts

In both methods, we found that the greatest common factor of 30 and 42 is 6. This means that 6 is the largest number that can divide both 30 and 42 evenly. Understanding how to find the GCF is useful in various mathematical applications, such as simplifying fractions or solving problems involving ratios. If you have any more questions about GCF or related topics, feel free to ask!