Factors · Factors · 1.4

Divisible by 4 and 6.

Some rules combine others: a number is divisible by 6 if it’s divisible by BOTH 2 and 3; divisible by 4 if its last two digits form a multiple of 4.

01 / THE IDEA

See it work.

Watch the method

Divisible by 4 and 6

124 → last two digits 24, a multiple of 4.

1 / 1
124  ?  ÷  4124\;?\;\div\;4
1

Divisibility by 4

Check: the last two digits form a multiple of 4.

124÷4⇒yes124 \div 4 \Rightarrow \text{yes}
— / WHY IT WORKS

The idea underneath.

Built from smaller rules

÷6 needs both the ÷2 and ÷3 tests; ÷4 looks at the last two digits.

Why it works

24 is a multiple of 4, so 124 is too.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Is 587 divisible by 4? (the last two digits form a multiple of 4)

1

Answer

No

EX 2medium

Is 913 divisible by 4? (the last two digits form a multiple of 4)

1

Answer

No

EX 3hard

Is 271 divisible by 2? (the last digit is even)

1

Answer

No

04 / COMMON TRAPS

Where students slip.

Trap

Checking only ÷2 for ÷6.

Fix

÷6 needs ÷2 AND ÷3.

Trap

Using the whole number for ÷4.

Fix

Just the last two digits.

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 837 divisible by 3? (the digit sum is divisible by 3)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
C2

Is 934 divisible by 9? (the digit sum is divisible by 9)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
C3

Is 771 divisible by 9? (the digit sum is divisible by 9)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
C4

Is 449 divisible by 2? (the last digit is even)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
Apply

Apply (4)

A1

Is 546 divisible by 4? (the last two digits form a multiple of 4)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
A2

Is 573 divisible by 2? (the last digit is even)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
A3

Is 627 divisible by 10? (the last digit is 0)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
A4

Is 349 divisible by 6? (it is divisible by both 2 and 3)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
Extension

Extension (4)

E1

Is 456 divisible by 3? (the digit sum is divisible by 3)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
E2

Is 651 divisible by 5? (the last digit is 0 or 5)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
E3

Is 962 divisible by 2? (the last digit is even)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.
E4

Is 672 divisible by 2? (the last digit is even)

Need a hint?
  • For 6, test 2 and 3.
  • For 4, check the last two digits.