Divisibility Decoder Anchor Chart
÷
Divisibility Decoder
Rules 2 – 10
Quick tests to know if a number divides evenly with no remainder!
Divisible Definition Remainder = 0
2
Divisible by 2
Last Digit Strategy
Must be Even
The last digit is even (ends in 0, 2, 4, 6, 8).
1,358 ✓ Ends in 8
427 ✗ Odd (7)
3
Divisible by 3
Sum of Digits Strategy
Sum ÷ 3
The sum of all digits is divisible by 3.
453 → 12 ✓ 12 ÷ 3 = 4
715 → 13 ✗ 13 not ÷ 3
4
Divisible by 4
Last 2 Digits Strategy
Last 2 ÷ 4
The number formed by the last two digits divides by 4.
3,524 ✓ 24 ÷ 4 = 6
819 ✗ 19 not ÷ 4
5
Divisible by 5
Last Digit Strategy
Ends in 0 or 5
The last digit is simply 0 or 5.
1,945 ✓ Ends in 5
673 ✗ Ends in 3
6
Divisible by 6
Combo Strategy
Both 2 AND 3
Divisible by both 2 AND 3 (it must be even AND digits sum to ÷ 3).
738 → 18 ✓ Even + sum=18
322 → 7 ✗ Even, sum≠3
7
Divisible by 7
Double & Subtract
Tricky Rule!
Double last digit, subtract from rest. Result is 0 or divides by 7.
343 → 34-(2×3) ✓ 28 ÷ 7 = 4
247 → 24-(2×7) ✗ 10 not ÷ 7
8
Divisible by 8
Last 3 Digits Strategy
Last 3 ÷ 8
The number formed by the last 3 digits is divisible by 8.
5,128 ✓ 128 ÷ 8 = 16
3,214 ✗ 214 not ÷ 8
9
Divisible by 9
Sum of Digits Strategy
Sum ÷ 9
The sum of all digits is divisible by 9.
7,533 → 18 ✓ 18 ÷ 9 = 2
642 → 12 ✗ 12 not ÷ 9
10
Divisible by 10
Last Digit Strategy
Ends in 0
The last digit is always an exact 0.
4,890 ✓ Ends in 0
5,005 ✗ Ends in 5
★
Memory Shortcuts
3 Pattern Families
● End Digits: 2, 5, 10 (last 1), 4 (last 2), 8 (last 3).
● Add the Digits: 3 and 9 sum up!
● Odd Number Alert: Odd numbers never ÷ 2, 4, 6, 8!
Always check if a number is even first!
Golden Rule: If a number is divisible by 9, it is ALWAYS divisible by 3!
Even + Divisible by 3 = Divisible by 6
