Grade 4 number sense lesson
Divisible by 8: Last Three Digits Trick, Examples, Chart, and Practice
A whole number is divisible by 8 when it can be divided into eight equal groups with no remainder. The fastest trick is to check the last three digits.
What does divisible by 8 mean?
A number is divisible by 8 if you can divide it by 8 evenly.
Evenly means there is no remainder.
For example, 64 is divisible by 8 because 64 / 8 = 8 with no remainder.
But 66 is not divisible by 8 because 66 / 8 leaves 2 left over.
You can also think of it as making eight equal groups. If the groups are equal and nothing is left over, the number is divisible by 8.
Printable Divisible by 8 trick chart
Use this SumReflex chart to remember the last-three-digits trick for divisibility by 8.
The same chart is also available in the Printable Number Reference Charts section with print and download buttons.
The last three digits trick
To check if a whole number is divisible by 8, look at the last three digits.
If the last three digits make a number divisible by 8, the whole number is divisible by 8.
If the last three digits do not make a number divisible by 8, the whole number is not divisible by 8.
For example, 12,344 ends in 344. Since 344 / 8 = 43, 12,344 is divisible by 8.
How the last digit helps, but does not finish the test
A number divisible by 8 must also be divisible by 2.
That means the last digit must be even: 0, 2, 4, 6, or 8.
So, if the last digit is odd, you can stop right away. The number is not divisible by 8.
But an even last digit is only a clue. It is not the full rule.
Example: 122 ends in 2, so it is even, but 122 is not divisible by 8.
Endings that show divisibility by 8
The last three digits must make a multiple of 8.
Early endings that work include 000, 008, 016, 024, 032, 040, 048, 056, 064, 072, 080, 088, 096, 104, 112, 120, 128, 136, 144, and 152.
The pattern keeps going by adding 8 each time, all the way to 992.
Example: 5,128 ends in 128. Since 128 / 8 = 16, 5,128 is divisible by 8.
Why does the trick work?
The trick works because 1,000 is divisible by 8.
1,000 / 8 = 125, so every full group of one thousand is safe for dividing by 8.
That means the thousands, ten-thousands, hundred-thousands, and larger place values do not decide the remainder.
Only the final three digits decide whether the whole number divides evenly by 8.
Step-by-step method
Step 1: Look at the last digit. If it is odd, the number is not divisible by 8.
Step 2: If the last digit is even, look at the last three digits.
Step 3: Check whether those last three digits are divisible by 8.
Step 4: If the last three digits divide evenly by 8, the original number is divisible by 8.
Example: 5,128 ends in 128. Since 128 / 8 = 16, 5,128 is divisible by 8.
Examples with solutions
Example 1: Is 1,024 divisible by 8? The last three digits are 024, which means 24. Since 24 / 8 = 3, 1,024 is divisible by 8. 1,024 / 8 = 128.
Example 2: Is 12,344 divisible by 8? The last three digits are 344. Since 344 / 8 = 43, 12,344 is divisible by 8. 12,344 / 8 = 1,543.
Example 3: Is 7,218 divisible by 8? The last three digits are 218. Since 218 is not divisible by 8, 7,218 is not divisible by 8.
Example 4: Is 5,128 divisible by 8? The last three digits are 128. Since 128 / 8 = 16, 5,128 is divisible by 8. 5,128 / 8 = 641.
Example 5: Is 3,006 divisible by 8? The last three digits are 006, which means 6. Since 6 is not divisible by 8, 3,006 is not divisible by 8.
Example 6: Is 9,992 divisible by 8? The last three digits are 992. Since 992 / 8 = 124, 9,992 is divisible by 8. 9,992 / 8 = 1,249.
Tougher examples
Example: Is 48,736 divisible by 8? The last three digits are 736. Since 736 / 8 = 92, 48,736 is divisible by 8.
Example: Is 91,426 divisible by 8? The last three digits are 426. Since 426 is not divisible by 8, 91,426 is not divisible by 8.
Example: Is 100,000 divisible by 8? The last three digits are 000. Since 000 is divisible by 8, 100,000 is divisible by 8.
Example: Is 4,444 divisible by 8? The last three digits are 444. Since 444 is not divisible by 8, 4,444 is not divisible by 8.
Word problem examples
Example: A teacher has 1,024 counters and wants to split them equally into 8 boxes. Can she do it? The last three digits are 024. Since 24 / 8 = 3, yes. Each box gets 128 counters.
Example: There are 7,218 stickers. Can 8 students share them equally with none left over? The last three digits are 218. Since 218 is not divisible by 8, no.
Example: A game has 5,128 points to divide equally among 8 teams. The last three digits are 128. Since 128 / 8 = 16, each team gets 641 points.
Common mistakes
Do not check only the last digit. The last digit rule is enough for divisibility by 2, but not for divisibility by 8.
Do not check only the last two digits. The last two digits rule is for divisibility by 4, not 8.
Do not ignore leading zeros in the final three digits. For 1,024, the last three digits are 024, which means 24.
Do not forget that 000 works. A whole number ending in 000 is divisible by 8.
Quick practice
1. Is 104 divisible by 8? Answer: yes, because 104 / 8 = 13.
2. Is 218 divisible by 8? Answer: no, because 218 is not divisible by 8.
3. Is 320 divisible by 8? Answer: yes, because 320 / 8 = 40.
4. Is 1,024 divisible by 8? Answer: yes, because the last three digits are 024, and 24 / 8 = 3.
5. Is 2,222 divisible by 8? Answer: no, because the last three digits, 222, are not divisible by 8.
6. Is 5,128 divisible by 8? Answer: yes, because 128 / 8 = 16.
7. Is 9,992 divisible by 8? Answer: yes, because 992 / 8 = 124.
The big idea
Divisibility by 8 is a last-three-digits rule.
An odd last digit means the number is not divisible by 8.
An even last digit only tells you to keep checking.
To finish the test, check whether the final three digits make a number divisible by 8.