Grade 4 number sense lesson
Divisible by 7: Double-and-Subtract Trick, Examples, Chart, and Practice
A whole number is divisible by 7 when it can be divided into seven equal groups with no remainder. A useful trick is to double the last digit and subtract it from the rest of the number.
What does divisible by 7 mean?
A number is divisible by 7 if you can divide it by 7 evenly.
Evenly means there is no remainder.
For example, 56 is divisible by 7 because 56 / 7 = 8 with no remainder.
But 58 is not divisible by 7 because 58 / 7 leaves 2 left over.
You can also think of it as making seven equal groups. If the groups are equal and nothing is left over, the number is divisible by 7.
Printable Divisible by 7 trick chart
Use this SumReflex chart to remember the double-and-subtract trick for divisibility by 7.
The same chart is also available in the Printable Number Reference Charts section with print and download buttons.
The double-and-subtract trick
To check if a whole number is divisible by 7, use this trick:
Step 1: Take the last digit away from the rest of the number.
Step 2: Double the last digit.
Step 3: Subtract that doubled value from the rest of the number.
Step 4: If the result is divisible by 7, the original number is divisible by 7.
Example: 203 has rest 20 and last digit 3. Double 3 to get 6. Then 20 - 6 = 14. Since 14 is divisible by 7, 203 is divisible by 7.
This is not a last-digit rule
Divisibility by 7 cannot be decided by the last digit alone.
For example, 14 and 24 both end in 4, but 14 is divisible by 7 and 24 is not.
The last digit is only one part of the trick. You must double it and subtract from the rest of the number.
This is different from divisibility by 2, where the last digit can decide whether a number is even.
Multiples of 7 to remember
Useful multiples of 7 are 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98.
When the trick gives one of these results, the original number is divisible by 7.
You may also get a larger number. If that happens, repeat the same trick again.
Example: 1,001 gives 100 - 2 = 98. Since 98 is a multiple of 7, 1,001 is divisible by 7.
Why does the trick work?
The double-and-subtract trick works because it keeps the same divisibility-by-7 result in a smaller number.
When you remove the last digit, you are separating the number into a tens part and a ones part.
The special subtract-double step changes the number but keeps the answer to the divisibility question the same.
That is why you can keep repeating the trick until the number is small enough to recognize as a multiple of 7 or not.
Step-by-step method
Step 1: Split the number into the rest of the number and the last digit.
Step 2: Double the last digit.
Step 3: Subtract the doubled digit from the rest of the number.
Step 4: Check whether the result is a multiple of 7.
Step 5: If the result is still large, repeat the same trick.
Example: For 371, the rest is 37 and the last digit is 1. Double 1 to get 2. Then 37 - 2 = 35. Since 35 is divisible by 7, 371 is divisible by 7.
Examples with solutions
Example 1: Is 203 divisible by 7? Rest 20, last digit 3. Double 3 to get 6. 20 - 6 = 14. Since 14 is divisible by 7, 203 is divisible by 7. 203 / 7 = 29.
Example 2: Is 371 divisible by 7? Rest 37, last digit 1. Double 1 to get 2. 37 - 2 = 35. Since 35 is divisible by 7, 371 is divisible by 7. 371 / 7 = 53.
Example 3: Is 672 divisible by 7? Rest 67, last digit 2. Double 2 to get 4. 67 - 4 = 63. Since 63 is divisible by 7, 672 is divisible by 7. 672 / 7 = 96.
Example 4: Is 705 divisible by 7? Rest 70, last digit 5. Double 5 to get 10. 70 - 10 = 60. Since 60 is not divisible by 7, 705 is not divisible by 7.
Example 5: Is 1,001 divisible by 7? Rest 100, last digit 1. Double 1 to get 2. 100 - 2 = 98. Since 98 is divisible by 7, 1,001 is divisible by 7. 1,001 / 7 = 143.
Example 6: Is 1,234 divisible by 7? Rest 123, last digit 4. Double 4 to get 8. 123 - 8 = 115. Repeat: rest 11, last digit 5, double 5 to get 10, and 11 - 10 = 1. Since 1 is not divisible by 7, 1,234 is not divisible by 7.
Tougher examples
Example: Is 2,618 divisible by 7? Rest 261, last digit 8. 261 - 16 = 245. Repeat: 24 - 10 = 14. Since 14 is divisible by 7, 2,618 is divisible by 7.
Example: Is 3,514 divisible by 7? Rest 351, last digit 4. 351 - 8 = 343. Since 343 is divisible by 7, 3,514 is divisible by 7.
Example: Is 4,444 divisible by 7? Rest 444, last digit 4. 444 - 8 = 436. Repeat: 43 - 12 = 31. Since 31 is not divisible by 7, 4,444 is not divisible by 7.
Example: Is 9,994 divisible by 7? Rest 999, last digit 4. 999 - 8 = 991. Repeat: 99 - 2 = 97. Since 97 is not divisible by 7, 9,994 is not divisible by 7.
Word problem examples
Example: A teacher has 203 counters and wants to split them equally into 7 boxes. Can she do it? Use the trick: 20 - 6 = 14. Yes, because 14 is divisible by 7. Each box gets 29 counters.
Example: There are 371 stickers. Can 7 students share them equally with none left over? Use the trick: 37 - 2 = 35. Yes, each student gets 53 stickers.
Example: A game has 705 points to divide equally among 7 teams. Use the trick: 70 - 10 = 60. Since 60 is not divisible by 7, the points cannot be shared equally among 7 teams.
Common mistakes
Do not check only the last digit. Divisibility by 7 does not work that way.
Do not forget to double the last digit before subtracting. For 203, you subtract 6, not 3.
Do not subtract in the wrong direction. Use rest of number minus double the last digit.
Do not stop too early when the result is still large. Repeat the same trick until the number is easy to judge.
Quick practice
1. Is 84 divisible by 7? Answer: yes, because 84 / 7 = 12.
2. Is 203 divisible by 7? Answer: yes, because 20 - 6 = 14.
3. Is 245 divisible by 7? Answer: yes, because 24 - 10 = 14.
4. Is 312 divisible by 7? Answer: no, because 31 - 4 = 27, and 27 is not divisible by 7.
5. Is 371 divisible by 7? Answer: yes, because 37 - 2 = 35.
6. Is 1,001 divisible by 7? Answer: yes, because 100 - 2 = 98.
7. Is 1,234 divisible by 7? Answer: no, because the repeated trick gives 1.
The big idea
Divisibility by 7 uses the double-and-subtract trick.
Split off the last digit, double it, and subtract that from the rest of the number.
If the result is divisible by 7, the original number is divisible by 7.
If the result is still large, repeat the trick until the answer is clear.