Divisibility Rules - 3, 6, 9 05:18 minutes

Video Transcript

Transcript Divisibility Rules - 3, 6, 9

There’s a hot new game that’s got everyone playing! It’s called: Creature Capture. Each player’s objective is to capture and then train the creatures they find. Players receive points for victories and can use those points in order to level up their creatures. Meet Olivia. She’s been playing Creature Capture for a few weeks now.

She’s just finished a battle with one of her friends and has some experience points to spend. The creatures in the game can be leveled up in three categories: Health, Attack and Defense. There’s just one catch: Players can only add points to the different categories using the Divisibility Rules for 3, 6 and 9. Players can increase the Health of their characters if the total number of points they have is divisible by 3.They can increase their Attack if their point total is divisible by 6. And finally, if their total is divisible by 9, players can increase their character’s defense.

Olivia has 348 points to spend, but which of her character’s abilities can Olivia increase?Let’s help Olivia upgrade her character. Is 348 divisible by 3? 6? 9? Is there a quick way to find out without having to use long division each time? Yes!

The Divisibility Rule for 3

There are so-called "divisibility rules" that help you determining whether a certain number is divisible by a number 1-10. The divisibility rules for 3 and 9 are quite similar. First, find the sum of all the digits in the number. For 348, you have to add 3 + 4 + 8. Doing so gives us 15.

If the resulting sum is divisible by 3, then the whole number is also divisible by 3. In this case, 3 goes into 15 exactly 5 times, so we can say that 15 is divisible by 3. This also means that 348 is divisible by 3!

The Divisibility Rule for 9

Olivia can upgrade her creature’s Health. But to figure out all her options, she checks if she can upgrade her creature's defense instead. Again, find the sum of all the digits in the number. As we already know, 3 + 4 + 8 is equal to 15. Since 15 divided by 9 gives you 1 and a remainder of 6, you know it isn't evenly divisible by 9. So we know that 348 is not divisible by 9. So Olivia cannot upgrade her creature's defense. Olivia is curious if she can level up her character's Attack.

The Divisibility Rule for 9

If Olivia wants her character to pack a more powerful punch, 348 has to be divisible by 6. But, how can you tell if a number is divisible by 6? It's easy! If a number is divisible by 2 and 3, it is also divisible by 6. First, check to see if the number is even. If it is, you can be sure that it's also divisible by 2. Since 348 ends in an 8, 348 is an even number! Next, check to see if the number is divisible by 3. You know already that 348 is divisible by 3. So, because the answer to both of these questions is yes, 348 is divisible by 6. Olivia can either level up Attack, or health.

Summary of the Divisibility Rules

Let's summarize the divisibility rules:

  • A number is divisible by 3 if the sum of its digits is divisible by 3.
  • A number is divisible by 9 if the sum of its digits is divisible by 9.
  • And a number is divisible by 6 if it is divisible by 2 (even number) and by 3. Back to the game.

Olivia decides to increase her character’s Attack. She just got challenged by a gamer who goes by the tag -=13urntK00k!ez=-. Let’s see how well Olivia does with her improved character!
Oh no, he attacks first. What an impressive attack!! Maybe Olivia should have upgraded her character's Health or Defense instead. Who is this gifted gamer? Granny?