Divisibility Rule of 7 with Examples

Last Updated : 23 Jul, 2025

Divisibility rules are simple mathematical shortcuts that help determine whether a number can be divided by another number without performing the actual division. In the case of 7, the divisibility rule for 7 helps us quickly determine if a number is divisible by 7 without needing to perform long division.

Divisibility Rule of 7:
Take the last digit (unit digit) of the number and double it.
Subtract this doubled value from the rest of the digits in the number.
Check the result: If the difference is divisible by 7 (or is 0), then the original number is divisible by 7.

More Examples on Divisibility by 7 Rule

Here are a few examples of numbers divisible by 7, applying the divisibility rule:

For 196:

Take the last digit (6), and double it to get 12.
Subtract 12 from 19 (remaining digits): 19 − 12 = 7.
Since 7 is divisible by 7, 196 is divisible by 7.

For 357:

Double the last digit (7) to get 14.
Subtract 14 from 35: 35 − 14 = 21.
Since 21 is divisible by 7, 357 is divisible by 7.

Divisibility Rule of 7 Proof

A general number N can be written as:

Here, are the digits of the number. We want to show that N is divisible by 7, i.e., N = 7k for some integer k.

We can factor out 10 from all terms except the last one, giving:

Now, to introduce the rule of subtracting twice the last digit, we add and subtract

This simplifies to:

Now, notice that:

so the term contributes nothing to the remainder modulo 7.
We only need to check whether

(mod 7)

since 10 ≡ 3 (mod 7), for N to be divisible by 7, (mod 7)

Divisibility Rule of 7 Solved Questions

Example 1: Check if the given number is divisible by 7 or not: 458409

Solution:

Let us check if the given number, 458409 is divisible by 7 or not using the following steps:
Step 1: We first take the last digit and multiply it by 2. So,(9 × 2 = 18).
Subtract 18 with the rest of the number, which is 45840. So, 45840 - 18 = 45822.
We are not sure if 45822 is a multiple of 7.
Step 2: We repeat the same process again with 45822.
Multiply the last digit by 2. So, (2 × 2 = 4).
Subtract 4 with the rest of the number, which is 4582. So, 4582 - 4 = 4578.
We are not sure if 4578 is a multiple of 7.
Step 3: Let us repeat the process again with 4578.
Multiply the last digit by 2. So, (8 × 2 = 16).
Subtract 16 with the rest of the number, which is 457. So, 457 - 16 = 441.
We are not sure if 441 is a multiple of 7.
Step 4: Let us repeat the process again with 441.
Multiply the last digit by 2. So, (1 × 2 = 2).
Subtract 2 with the rest of the number, which is 44. So, 44 - 2 = 42.
42 is the sixth multiple of 7.
Therefore, we can confirm that 458409 is divisible by 7.

Example 2: Is 154 divisible by 7?

Solution:

The last digit in the given number 15 4 (unit digit ) is 4.
We now use the given number without the last digit which is 15.
Subtract twice the last digit 4 from 15:
15 - 2 (4) = 15 - 8 = 7
The result 7 is a multiple of 7 and therefore 154 is divisible by 7.

Example 3: Consider the number: 308. Check if it is divisible by 7.

Solution:

Following the rule:
Double of the last digit =16
Subtracting the result from the rest of the number; 30-16 =14
14 is a multiple of 7, hence the number is divisible by 7.

Example 4: Which of the following numbers is divisible by 7?

171
119
107
383

Solution:

The correct answer is option (b) 119.
Explanation:
(a) 171
Step 1: Double the unit digit = 1 x 2 = 2
Step 2: Difference = 17 – 2 = 15
15 is not a multiple of 7, and hence 171 is not divisible by 7.
(b) 119
Step 1: Double the unit digit = 9 x 2 = 18
Step 2: Difference = 11 – 18 = -7, which is a multiple of 7
Hence, 119 is divisible by 7.
(c) 107
Step 1: Double the unit digit = 7 x 2 = 14
Step 2: Difference = 10 – 14 = -4, which is not a multiple of 7.
Hence, 107 is not divisible by 7.
(d) 383
Step 1: Double the unit digit = 3 x 2 = 6
Step 2: Difference = 38 – 6 = 32, which is not a multiple of 7.
Thus, 383 is not divisible by 7.

Example 5: Check whether a number 449 is divisible by 7.

Solution:

Given number = 449.
To check whether a number 449 is divisible by 7, follow the below steps.
Step 1: Double the unit digit = 9 x 2 = 18
Step 2: Take the difference between the remaining part of the given number and the result obtained from step 1. (i.e., 18)
= 44 – 18
= 26, which is not a multiple of 7.
Hence, the given number 449 is not divisible by 7.

Divisibility Rule of 7 Worksheet

1. Determine whether the number 203 is divisible by 7.

2. Is the number 1,218 divisible by 7? Show your calculation.

3. Find out if 5,643 is divisible by 7 using the divisibility rule.

4. Check if 2,118 is divisible by 7 and explain your reasoning.

5. Use the divisibility rule to determine if 9,374 is divisible by 7.

Conclusion

In this article, we discovered the method for determining if a number is divisible by 7 and the rule for divisibility by 7 is an important guideline that applies to all numbers. When divided by 7 there should be no remainder left after the division. This holds true because whenever we divide a number by 7 the outcome is consistently an even number. Keep practicing this divisibility rule to get a better grasp at the concept.

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