Divisibility rules: word problems
key notes:
What is Divisibility?
🔹 A number is divisible by another if it can be divided without any remainder.
🟢 Example: 12 ÷ 3 = 4 ✅ (12 is divisible by 3)
Divisibility Rules to Remember:
By 2️⃣: Last digit is 0, 2, 4, 6, or 8.
By 3️⃣: Sum of digits is divisible by 3.
By 4️⃣: Last two digits form a number divisible by 4.
By 5️⃣: Last digit is 0 or 5.
By 6️⃣: Divisible by both 2 and 3.
By 9️⃣: Sum of digits is divisible by 9.
By 10️⃣: Last digit is 0.
Tips for Word Problems 📝:
🔹 Read the problem carefully.
🔹 Identify which divisibility rule applies.
🔹 Check numbers using the rules before dividing.
🔹 Always write your remainder if any.
Common Word Problem Examples:
🍎 “There are 24 apples. Can we divide them into baskets of 3 without leftover?”
✅ 24 ÷ 3 = 8 → divisible
🎈 “There are 50 balloons. Can we make groups of 5?”
✅ 50 ÷ 5 = 10 → divisible
Fun Tip 🎉:
Use color codes in your notebook:
🔵 Blue for numbers divisible by 2
🔴 Red for numbers divisible by 3
🟢 Green for numbers divisible by 5
Quick Check Strategy ✅:
Add digits for 3 & 9
Look at the last digit for 2, 5, 10
Check last 2 digits for 4
Learn with an example
🔥 At the company picnic, 75 employees will participate in a relay race. Each team must be the same size.
How many teams could the company form for the relay race?
- 5
- 2
- 10
Which number evenly divides 75? Try each number.
First try the “divisible by 5” rule on 75.
Look at the ones digit:
75
The ones digit is 5.
The rule says that 75 is divisible by 5.
Next try the “divisible by 2” rule on 75.
Look at the ones digit:
75
The ones digit is 5.
The rule says that 75 is not divisible by 2.
Finally, try the “divisible by 10” rule on 75.
Look at the ones digit:
75
The ones digit is 5.
The rule says that 75 is not divisible by 10.
75 is divisible by 5. The company could form 5 teams.
🔥 Susan is arranging bottles of nail polish on her chest of drawers. She has 84 bottles and she wants to arrange the bottles so that there are the same number of bottles in each row.
How many bottles of nail polish could Susan put in each row?
- 5
- 10
- 2
Which number evenly divides 84? Try each number.
First try the “divisible by 5” rule on 84.
Look at the ones digit:
84
The ones digit is 4.
The rule says that 84 is not divisible by 5.
Next try the “divisible by 10” rule on 84.
Look at the ones digit:
84
The ones digit is 4.
The rule says that 84 is not divisible by 10.
Finally, try the “divisible by 2” rule on 84.
Look at the ones digit:
84
The ones digit is 4.
The rule says that 84 is divisible by 2.
84 is divisible by 2. Susan could put 2 bottles of nail polish in each row.
🔥 Bella wants to arrange 96 roses into vases. She wants to put the same number of roses in each vase without any roses left over.
How many vases could Bella use?
- 2
- 10
- 5
Which number evenly divides 96? Try each number.
First try the “divisible by 2” rule on 96.
Look at the ones digit:
96
The ones digit is 6.
The rule says that 96 is divisible by 2.
Next try the “divisible by 10” rule on 96.
Look at the ones digit:
96
The ones digit is 6.
The rule says that 96 is not divisible by 10.
Finally, try the “divisible by 5” rule on 96.
Look at the ones digit:
96
The ones digit is 6.
The rule says that 96 is not divisible by 5.
96 is divisible by 2. Bella could use 2 vases.
Let’s practice!
