The why of the 3 divisibility rule | Factors and multiples | Pre-Algebra | Khan Academy | Summary and Q&A

TL;DR

Learn how to quickly determine if a number is divisible by 3 using a simple trick.

Key Insights

• 🍹 Divisibility by 3 can be quickly determined by summing up the digits of a number.
• 😑 The trick relies on the fact that any number can be expressed as a sum of multiples of powers of 10.
• 🍹 The sum of the digits can be continuously reduced until a single-digit result is obtained for verification.
• 🚨 This technique can be useful in emergency situations where quick divisibility checks are required.
• 🍹 Divisibility by 3 is closely related to divisibility by 9, as both involve summing the digits.
• 🧑‍🏭 The trick is based on the fact that multiples of 10 and 9 are always divisible by 3.
• 🍹 The process can be easily extended to larger numbers by considering additional digits in the sum.

Transcript

You're just walking down the street and someone comes up to you and says "Quick! Quick!-- 4792. Is this divisible by 3? This is an emergency! Tell me as quickly as possible! And luckily you have a little tool in your toolkit where you know how to test for divisibility by 3 Well, you say I can just add up the digits If the sum of that is a multiple ... Read More

Questions & Answers

Q: How can you quickly determine if a number is divisible by 3?

You can add up all the individual digits of the number, and if the sum is divisible by 3, then the number itself is divisible by 3.

Q: What if the sum of the digits is not a single digit?

If the sum is not a single digit, you can repeat the process and continue summing the digits until a single-digit result is obtained.

Q: Why does this trick work?

This trick works because any number can be expressed as a sum of multiples of powers of 10, and the multiples of 10 are always divisible by 3.

Q: Can this trick be used to determine divisibility by other numbers?

This trick specifically applies to divisibility by 3, but similar techniques can be used for other numbers like 9 by summing the digits and verifying divisibility.

Summary & Key Takeaways

• By summing up the individual digits of a number, if the sum is divisible by 3, then the entire number is divisible by 3.

• You can verify divisibility by further summing the digits of the sum until a single-digit result is obtained.

• This trick works because any number can be written as a sum of multiples of powers of 10, where the multiples of 10 are always divisible by 3.