Concept 4 of 4
Quick Tests: The Divisibility Rules
Today's big idea
Some divisors are settled by the last digit, others by adding every digit.
2, 5 and 10 read the last digit. 3 and 9 read the digit sum instead.
How it works
👀 What's going on?
Does 3 divide 7,236? You could work through the division and find out. Or you could add 7 + 2 + 3 + 6, get 18, and know the answer before you have finished writing the sum down. For the most useful divisors there is a test like that, and it never needs the division at all.
💡 Here's the trick
Look at the cards above. Each card reads one small feature of a number and nothing else. For 2, 5 and 10 you read only the last digit. An even last digit means 2 divides it. A 0 or a 5 means 5 divides it, and a 0 means 10 does too. For 3 and 9 you ignore the digits' places and just add them up. If that total divides by 3, so does the whole number. If it divides by 9, so does the whole number.
🪄 How to do it
- 1.Find your divisor on the cards above.
- 2.Read only the part the card asks for, the last digit or the digit sum.
- 3.Say yes or no, and never do the division.
✍️ Try it
Does 3 divide 4,131? Then, does 5 divide 2,450?
Add the digits of 4,131 and you get 4 + 1 + 3 + 1 = 9. Since 3 divides 9, the answer is yes. Now 2,450 ends in a 0, so 5 divides it and the answer is yes again. That 0 also means 2 and 10 divide it.
⚠️ Watch out
You might be thinking that adding the digits works for every divisor. It works for 3 and 9 only. The digits of 14 add to 5, and 7 does divide 14, but 7 does not divide 5. Adding digits tells you nothing about 7.
🌟 Why this matters
Sharing 96 sweets between 3 friends works because 9 + 6 = 15 and 3 divides 15. You can settle that in your head before anyone opens the packet. The rules also turn factor hunting from a long chain of divisions into a handful of one-second checks.
Exam tip: A quick test rules out three wrong options before you work anything out.
See it in action
⚡ Time to play!
DOES 5 DIVIDE IT?
385
Tap the rule card for 5 to see which part of the number it reads.
Quick check
✅ VERIFICATION
Without dividing, which of these numbers is divisible by 9?
⚡ Finish the activity above first to answer.
Keep going!