Mental Math · Division · D4

Divisibility radar.

Before you divide, a few quick rules tell you whether a number divides evenly at all — by looking at its last digit or its digit sum. This 'radar' saves wasted effort and helps you simplify.

01 / THE METHOD

How to think about it.

Watch the method

Run the divisibility radar

Scan 360: it's even (÷2), ends in 0 (÷5 and ÷10), and its digits 3+6+0 = 9 (÷3 and ÷9). One look tells you a lot.

1 / 5
360360 = ?
1
360→2?360 \to 2?

Ends in 0, so it is divisible by 2 (even).

2
3+6+0=93+6+0 = 9

Digit sum is 9, a multiple of 3 → divisible by 3.

3
360→5?360 \to 5?

Ends in 0, so it is divisible by 5.

4
9→9?9 \to 9?

Digit sum 9 is a multiple of 9 → divisible by 9.

5
360→10?360 \to 10?

Ends in 0, so it is divisible by 10.

— / WHY IT WORKS

The idea underneath.

Last digit and digit sum

÷2: last digit even. ÷5: last digit 0 or 5. ÷10: last digit 0. ÷3: digit sum divisible by 3. ÷9: digit sum divisible by 9. ÷6: passes both the 2 rule and the 3 rule.

Why it works

You can judge a number's factors at a glance, without dividing.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Is 234 divisible by 3?

1

Digit sum

2 + 3 + 4 = 9.

2

Check

9 is a multiple of 3 → yes.

EX 2medium

Which of 2, 3, 5 divide 480?

1

Last digit 0

Even → ÷2; ends in 0 → ÷5.

2

Digit sum

4+8+0 = 12 → ÷3.

3

All three

2, 3, and 5 all divide 480.

EX 3hard

504 ÷ 9

1

Radar

5+0+4 = 9 → divisible by 9.

2

Divide

504 ÷ 9 = 56.

04 / COMMON TRAPS

Where students slip.

Trap

Thinking the ÷3 rule looks at the last digit.

Fix

÷3 and ÷9 use the DIGIT SUM, not the last digit. 471: 4+7+1 = 12 → divisible by 3.

Trap

Assuming even numbers are divisible by 4.

Fix

Even means ÷2, not necessarily ÷4. Check the last two digits for 4.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

372 is divisible by 3 (digits sum to 12). 372 ÷ 3 = ?

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
C2

456 ends in 6, so it's even. 456 ÷ 2 = ?

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
C3

415 ends in 5. 415 ÷ 5 = ?

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
C4

630 ends in 0. 630 ÷ 10 = ?

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
Apply

Apply (4)

A1

Is 234 divisible by 3? Type 1 for yes, 0 for no.

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
A2

Is 517 divisible by 3? Type 1 for yes, 0 for no.

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
A3

Is 480 divisible by 9? Type 1 for yes, 0 for no.

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
A4

Is 522 divisible by 9? Type 1 for yes, 0 for no.

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
Extension

Extension (4)

E1

504 ÷ 9 = ? (digits sum to 9)

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
E2

Is 1278 divisible by 6? Type 1 for yes, 0 for no.

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
E3

738 ÷ 6 = ? (even, digits sum to 18)

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.
E4

Is 2025 divisible by 5? Type 1 for yes, 0 for no.

Need a hint?
  • The last digit tells you about 2, 5, and 10.
  • The digit sum tells you about 3 and 9.