The divisibility rule of 7 is one of the most useful mathematical tricks used to check whether a number is exactly divisible by 7 or not. Divisibility rules help students solve arithmetic problems faster without performing long division. These rules are important in school mathematics, competitive exams, mental maths, and daily calculations.
Among all divisibility tests, the divisibility rule for 7 is considered slightly more difficult because it involves subtraction and repeated steps. However, once students understand the method properly, it becomes simple and easy to apply. Learning the divisibility rule of 7 also improves number sense and calculation speed.
Students from Class 6, Class 7, and Class 8 often study divisibility rules as part of the number system and factors and multiples chapter. The rule is also useful in higher classes and aptitude exams. In this article, you will learn the divisibility rule of 7 step by step with examples, shortcut tricks, solved questions, practice exercises, and comparison tables.
What is the Divisibility Rule of 7?
The divisibility rule of 7 is a mathematical method used to check whether a number can be divided by 7 completely without leaving any remainder.
According to the rule: Double the last digit of the number and subtract it from the remaining part of the number. If the result is divisible by 7, then the original number is also divisible by 7.
This process can be repeated until a small number is obtained.
Example 1: Check 203
- Last digit = 3
- Double of 3 = 6
- Remaining number = 20
- Subtract: 20 − 6 = 14
Since 14 is divisible by 7, 203 is also divisible by 7.
Example 2: Check 371
- Last digit = 1
- Double of 1 = 2
- Remaining number = 37
- Subtract: 37 − 2 = 35
Since 35 is divisible by 7, the number 371 is divisible by 7.
This divisibility test for 7 helps students avoid lengthy division methods.
Step-by-Step Method to Apply the Divisibility Rule of 7
Students can follow these simple steps to apply the rule correctly.
Steps of the Divisibility Rule of 7
- Separate the last digit from the number.
- Multiply the last digit by 2.
- Subtract the result from the remaining number.
- Repeat the process if the new number is large.
- Check whether the final result is divisible by 7.
Examples of Divisibility Rule of 7
| Number | Step | Result |
|---|---|---|
| 203 | 20 − (3 × 2) | 14 |
| 371 | 37 − (1 × 2) | 35 |
| 455 | 45 − (5 × 2) | 35 |
| 672 | 67 − (2 × 2) | 63 |
| 875 | 87 − (5 × 2) | 77 |
All the final results are divisible by 7. Therefore, all these numbers are divisible by 7.
Understanding the Logic Behind the Rule
Many students ask why the divisibility rule for 7 works. The rule is based on number properties and arithmetic operations. Instead of dividing the entire number by 7, the method reduces the number into smaller values while keeping the divisibility unchanged.
This process makes large numbers easier to handle mentally. That is why the divisibility rule of 7 is useful in mental maths and fast calculations.
Shortcut Trick for Divisibility Rule of 7
The divisibility rule of 7 can become easier with practice. Students can remember this quick trick:
“Double the last digit and subtract.”
This short sentence helps students recall the full process quickly during exams.
- Take the last digit
- Multiply by 2
- Subtract from the remaining number
- Repeat if needed
For example, check 301:
- Last digit = 1
- Double = 2
- Remaining number = 30
- 30 − 2 = 28
Since 28 is divisible by 7, 301 is divisible by 7.
This shortcut is very useful in competitive exams where speed matters.
Solved Examples on Divisibility Rule of 7
Example 1: Is 294 divisible by 7?
- Last digit = 4
- Double = 8
- Remaining number = 29
- 29 − 8 = 21
21 is divisible by 7.
Therefore, 294 is divisible by 7.
Example 2: Is 512 divisible by 7?
- Last digit = 2
- Double = 4
- Remaining number = 51
- 51 − 4 = 47
47 is not divisible by 7.
Therefore, 512 is not divisible by 7.
Example 3: Check 1001
- Last digit = 1
- Double = 2
- Remaining number = 100
- 100 − 2 = 98
98 is divisible by 7.
Therefore, 1001 is divisible by 7.
Example 4: Check 742
- Last digit = 2
- Double = 4
- Remaining number = 74
- 74 − 4 = 70
70 is divisible by 7.
Therefore, 742 is divisible by 7.
Example 5: Is 689 divisible by 7?
- Last digit = 9
- Double = 18
- Remaining number = 68
- 68 − 18 = 50
50 is not divisible by 7.
Therefore, 689 is not divisible by 7.
Example 6: Check 1617
- Last digit = 7
- Double = 14
- Remaining number = 161
- 161 − 14 = 147
147 is divisible by 7.
Therefore, 1617 is divisible by 7.
Example 7: Check 2450
- Last digit = 0
- Double = 0
- Remaining number = 245
- 245 − 0 = 245
245 is divisible by 7.
Therefore, 2450 is divisible by 7.
Example 8: Check 998
- Last digit = 8
- Double = 16
- Remaining number = 99
- 99 − 16 = 83
83 is not divisible by 7.
Therefore, 998 is not divisible by 7.
Practice Questions on Divisibility Rule of 7
Students should practice regularly to improve speed and accuracy.
- Is 343 divisible by 7?
- Check whether 742 is divisible by 7.
- Is 931 divisible by 7?
- Check whether 560 is divisible by 7.
- Is 1218 divisible by 7?
- Check whether 1498 is divisible by 7.
- Is 777 divisible by 7?
- Check whether 2800 is divisible by 7.
MCQs on Divisibility Rule of 7 Problems
1. Which of the following is divisible by 7?
A. 234
B. 343
C. 512
D. 998
Answer: B. 343
2. What is the first step in the divisibility rule of 7?
A. Add digits
B. Multiply all digits
C. Separate the last digit
D. Divide by 10
Answer: C. Separate the last digit
3. Is 455 divisible by 7?
A. Yes
B. No
Answer: A. Yes
Applications of Divisibility Rule of 7
The divisibility rule of 7 has many practical uses in mathematics and competitive exams.
Importance of Divisibility Rules
1. Faster Calculations: Students can quickly identify multiples of 7 without division.
2. Useful in Competitive Exams: Questions based on divisibility rules are common in aptitude tests.
3. Helpful in Mental Maths: The rule improves mental calculation speed.
4. Better Understanding of Number System: Students learn more about factors, multiples, and arithmetic properties.
5. Useful in Simplification Problems: Divisibility tests help simplify fractions and algebraic calculations.
Difference Between Divisibility Rules of 7 and Other Numbers
Different numbers have different divisibility tests. Some rules are simple while others require multiple steps.
| Number | Divisibility Rule |
|---|---|
| 2 | Last digit should be even |
| 3 | Sum of digits should be divisible by 3 |
| 4 | Last two digits should be divisible by 4 |
| 5 | Last digit should be 0 or 5 |
| 6 | Number should be divisible by both 2 and 3 |
| 7 | Double the last digit and subtract |
| 8 | Last three digits should be divisible by 8 |
| 9 | Sum of digits should be divisible by 9 |
| 10 | Last digit should be 0 |
| 11 | Difference of alternate digit sums should be divisible by 11 |
Among these rules, the divisibility rule for 7 requires repeated subtraction steps, which makes it slightly more advanced.
Tips to Learn Divisibility Rule of 7 Easily
Students can use the following tips to master the concept quickly.
- Practice at least 10 questions daily.
- Start with small numbers first.
- Learn multiplication tables of 7 properly.
- Use rough work for subtraction.
- Repeat the process slowly until confident.
- Compare answers with long division for checking.