Common divisibility examples | Factors and multiples | Pre-Algebra | Khan Academy

TL;DR

Learn how to determine the common factors and prime factorization of numbers to find their least common multiple.

Transcript

• [Voiceover] In this video I wanna do a bunch of example problems that show up on standardized exams and definitely will help you with our divisibility module because it's asking you questions like this. And this is just one of the examples. All numbers divisible by both 12 and 20 are also divisible by: And the trick here is to realize that if a n... Read More

Key Insights

• 🧑‍🏭 When determining if a number is divisible by multiple factors, check for the presence of each factor's prime factorization.
• #️⃣ The prime factorization of a number helps determine its divisibility by other numbers.
• 🧑‍🏭 The least common multiple of two numbers is found by multiplying their common prime factors.
• 🧑‍🏭 Any number divisible by both 12 and 20 must have the prime factors of 2, 2, 3, and 5.
• #️⃣ The least common multiple of 12 and 20 is 60, but there are other numbers that are divisible by both as well.
• #️⃣ The prime factorization of a number can help identify which numbers are divisible by it.
• #️⃣ Divisibility rules rely on prime factorizations to determine if a number is divisible by another number.

Questions & Answers

Q: How can you determine if a number is divisible by both 12 and 20?

To determine if a number is divisible by both 12 and 20, you need to check if its prime factorization includes 2, 2, 3, and 5.

Q: What is the least common multiple of 12 and 20?

The least common multiple of 12 and 20 is 60.

Q: Can a number be divisible by 12 and 20 without having the prime factors of 2, 2, 3, and 5?

No, any number divisible by both 12 and 20 must have the prime factors of 2, 2, 3, and 5.

Q: How can you determine if a number is divisible by 12 and 20 without finding its prime factorization?

If a number is divisible by both 12 and 20, it can be divided evenly by 60 without any remainders.

Summary & Key Takeaways

• The video explains how to determine whether a number is divisible by both 12 and 20 using prime factorization.

• The prime factorization of 12 is 2 x 2 x 3, and the prime factorization of 20 is 2 x 2 x 5.

• The least common multiple of 12 and 20 is 60, which means any number divisible by both must have prime factors of 2, 2, 3, and 5.