Factors · Factors · 1.3

Divisibility rules.

Quick tests tell you if a number divides evenly without dividing: even → ÷2; digit sum divisible by 3 → ÷3; ends in 0 or 5 → ÷5; digit sum divisible by 9 → ÷9; ends in 0 → ÷10.

01 / THE IDEA

See it work.

Watch the method

Divisibility rules

123 → 1+2+3 = 6, divisible by 3.

1 / 1
123  ?  ÷  3123\;?\;\div\;3
1

Divisibility by 3

Check: the digit sum is divisible by 3.

123÷3⇒yes123 \div 3 \Rightarrow \text{yes}
— / WHY IT WORKS

The idea underneath.

Test without dividing

Each small divisor has a shortcut: the last digit or the digit sum usually tells you.

Why it works

1+2+3 = 6 → 123 is divisible by 3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Is 513 divisible by 6? (it is divisible by both 2 and 3)

1

Answer

No

EX 2medium

Is 712 divisible by 4? (the last two digits form a multiple of 4)

1

Answer

Yes

EX 3hard

Is 549 divisible by 9? (the digit sum is divisible by 9)

1

Answer

Yes

04 / COMMON TRAPS

Where students slip.

Trap

Using the ÷3 rule for ÷9 or vice versa.

Fix

Digit sum ÷3 for 3; ÷9 for 9.

Trap

Checking the wrong digit.

Fix

÷5 looks at the LAST digit.

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

Is 525 divisible by 3? (the digit sum is divisible by 3)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
C2

Is 927 divisible by 2? (the last digit is even)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
C3

Is 485 divisible by 5? (the last digit is 0 or 5)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
C4

Is 885 divisible by 5? (the last digit is 0 or 5)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
Apply

Apply (4)

A1

Is 501 divisible by 10? (the last digit is 0)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
A2

Is 295 divisible by 6? (it is divisible by both 2 and 3)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
A3

Is 951 divisible by 5? (the last digit is 0 or 5)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
A4

Is 443 divisible by 9? (the digit sum is divisible by 9)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
Extension

Extension (4)

E1

Is 592 divisible by 5? (the last digit is 0 or 5)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
E2

Is 414 divisible by 10? (the last digit is 0)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
E3

Is 150 divisible by 2? (the last digit is even)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.
E4

Is 458 divisible by 3? (the digit sum is divisible by 3)

Need a hint?
  • Use the last digit or the digit sum.
  • Match the rule to the divisor.