Greatest common factor exercise | Factors and multiples | Pre-Algebra | Khan Academy

TL;DR

The greatest common divisor (GCD) is the largest number that can evenly divide into two given numbers.

Transcript

We're asked, what is the greatest common divisor of 20 and 40? And they just say, another way to say this is the GCD, or greatest common divisor, of 20 of 40 is equal to question mark. And greatest common divisor sounds like a very fancy term, but it's really just saying, what is the largest number that is divisible into both 20 and 40? Well, this ... Read More

Key Insights

• #️⃣ The GCD is the largest number that evenly divides two given numbers.
• 👂 The GCD can be found by listing the factors or using prime factorization.
• #️⃣ If one number is a multiple of the other, the GCD is equal to the smaller number.
• 🧑‍🏭 If there are no common factors other than 1, the GCD is 1.
• #️⃣ The GCD of two prime numbers is always 1.
• 🌥️ Using prime factorization can simplify finding the GCD for larger numbers.
• 🛩️ The GCD cannot be larger than the smaller number.

Questions & Answers

Q: What is the definition of the greatest common divisor (GCD)?

The GCD is the largest number that can divide two given numbers without a remainder.

Q: How can the GCD of two numbers be found without listing all the factors?

Another approach is using prime factorization. By finding the common prime factors of the given numbers, the GCD can be determined.

Q: Can the GCD ever be larger than the smaller of the two given numbers?

No, because the GCD must be a factor of both numbers, and it cannot be larger than any of the factors of the smaller number.

Q: What is the GCD of two prime numbers?

If the given numbers are prime, the only common factor is 1, so the GCD will always be 1.

Summary & Key Takeaways

• The GCD of 20 and 40 is 20 because 20 is a factor of both numbers.

• The GCD of 10 and 7 is 1 because they have no common factors other than 1.

• The GCD of 21 and 30 can be found by listing the factors or using prime factorization, in this case, the GCD is 3.