How To Find The Greatest Common Factor Quickly! | Summary and Q&A

TL;DR

Learn how to find the greatest common factor (GCF) of two or more numbers by identifying their prime factorizations and finding the common prime factors.

Key Insights

• #️⃣ The greatest common factor (GCF) is the largest number that divides evenly into two or more given numbers.
• 🧑‍🏭 To find the GCF, determine the prime factorizations of the numbers and identify the common prime factors.
• #️⃣ The GCF can be larger than the smallest number and does not have to be a prime number.
• 🧑‍🏭 When variables are involved, treat them as additional factors and include them in the prime factorization.

Transcript

in this lesson we're going to talk about how to find the greatest common factor so let's say if we have two numbers 15 and 35 what is the greatest common factor between these two numbers here's one method that you can use first write the prime factorization of each number the prime factorization of 15 is simply 3 times 5. you want to break down 15 ... Read More

Questions & Answers

Q: What is the process for finding the greatest common factor (GCF)?

The process involves writing the prime factorization of each number and identifying the common prime factors. The largest common factor is the GCF.

Q: How do you find the GCF of 15 and 35?

The prime factorization of 15 is 3 * 5, and the prime factorization of 35 is 5 * 7. The common prime factor is 5, making it the GCF.

Q: Can the GCF be larger than the smallest number in a given set?

Yes, the GCF can be larger than the smallest number. It is simply the largest number that divides evenly into all the given numbers.

Q: Does the GCF have to be a prime number?

No, the GCF can be any positive integer. However, it is often expressed as the product of prime factors.

Q: What is the GCF of 12 and 16?

The prime factorization of 12 is 2 * 2 * 3, and the prime factorization of 16 is 2 * 2 * 2 * 2. The common prime factors are two twos, making it the GCF.

Q: How do you find the GCF when variables are involved?

The process is the same. Write the prime factorizations of each expression, including the variables, and identify the common factors.

Q: What is the GCF of 6x and 9x^2?

The prime factorization of 6x is 2 * 3 * x, and the prime factorization of 9x^2 is 3 * 3 * x * x. The common factors are 3 and x, making them the GCF.

Q: Can the GCF be different for each pair of numbers in a set?

Yes, the GCF can be different for each pair of numbers. Each pair may have different prime factors, resulting in different GCFs.

Summary & Key Takeaways

• The greatest common factor (GCF) is the largest number that divides evenly into two or more given numbers.

• To find the GCF, first, write the prime factorizations of each number.

• Identify the common prime factors in the factorizations and the largest common factor is the GCF.