Hello Year 5! Today, we’re going to learn about divisibility by 3, 6, and 9. This means we’ll figure out how to tell if a number can be divided evenly by these numbers. Let’s get started!
What is Divisibility?
Divisibility is when one number can be divided by another number without leaving a remainder. For example, if we can divide 12 by 3 and get 4 with nothing left over, we say that 12 is divisible by 3.
Divisibility by 3
Key Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
Example
- Look at the number 123.
- Add the digits: ( 1 + 2 + 3 = 6 ).
- Since 6 is divisible by 3, the number 123 is also divisible by 3!
Divisibility by 6
Key Rule: A number is divisible by 6 if it is divisible by both 2 and 3.
- Divisible by 2: A number is divisible by 2 if it ends in an even digit (0, 2, 4, 6, 8).
- Divisible by 3: Use the rule we learned above.
Example
- Look at the number 24.
- It ends in 4 (even), so it is divisible by 2.
- Add the digits: ( 2 + 4 = 6 ) (divisible by 3).
- Since 24 is divisible by both 2 and 3, it is also divisible by 6!
Divisibility by 9
Key Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.
Example
- Look at the number 252.
- Add the digits: ( 2 + 5 + 2 = 9 ).
- Since 9 is divisible by 9, the number 252 is also divisible by 9!
Tips and Tricks
- To check for divisibility by 3 or 9, always add the digits together.
- For 6, remember to check for both evenness (divisible by 2) and the sum of digits (divisible by 3).
- Practice with different numbers to get better at spotting patterns!
Questions
Easy Level
- Is 15 divisible by 3?
- Is 18 divisible by 3?
- Is 24 divisible by 6?
- Is 30 divisible by 3?
- Is 42 divisible by 6?
- Is 27 divisible by 9?
- Is 12 divisible by 6?
- Is 21 divisible by 3?
- Is 36 divisible by 9?
- Is 48 divisible by 6?
- Is 9 divisible by 3?
- Is 54 divisible by 9?
- Is 60 divisible by 6?
- Is 81 divisible by 9?
- Is 63 divisible by 3?
- Is 72 divisible by 6?
- Is 30 divisible by 9?
- Is 45 divisible by 3?
- Is 27 divisible by 3?
- Is 90 divisible by 6?
Medium Level
- Is 123 divisible by 3?
- Is 156 divisible by 6?
- Is 81 divisible by 9?
- Is 234 divisible by 3?
- Is 390 divisible by 6?
- Is 888 divisible by 9?
- Is 465 divisible by 3?
- Is 546 divisible by 6?
- Is 729 divisible by 9?
- Is 912 divisible by 3?
- Is 105 divisible by 3?
- Is 462 divisible by 6?
- Is 234 divisible by 9?
- Is 306 divisible by 3?
- Is 513 divisible by 9?
- Is 978 divisible by 6?
- Is 333 divisible by 3?
- Is 234 divisible by 6?
- Is 486 divisible by 9?
- Is 672 divisible by 6?
Hard Level
- Is 12345 divisible by 3?
- Is 34560 divisible by 6?
- Is 987654 divisible by 9?
- Is 23456 divisible by 3?
- Is 87654 divisible by 6?
- Is 54321 divisible by 3?
- Is 111111 divisible by 9?
- Is 222222 divisible by 6?
- Is 999999 divisible by 3?
- Is 67890 divisible by 6?
- Is 13579 divisible by 3?
- Is 888888 divisible by 9?
- Is 24680 divisible by 6?
- Is 121212 divisible by 3?
- Is 555555 divisible by 9?
- Is 444444 divisible by 6?
- Is 121212 divisible by 3?
- Is 777777 divisible by 9?
- Is 999999 divisible by 6?
- Is 123456 divisible by 3?
Answers and Explanations
Easy Level Answers
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- No
- Yes
- Yes
- Yes
Medium Level Answers
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- No
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
Hard Level Answers
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- No
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- Yes
- No
- Yes
Remember, practice makes perfect! Keep trying out different numbers, and you’ll get better at understanding divisibility. Happy learning!
