Divisibility Rule of 7
A number is said to be divisible by 7 if the remainder is zero and the quotient is a whole number. The 'Divisibility rule' or 'Divisibility test' helps us to check if a number is completely divisible by another number without actually doing the division. The divisibility rule for 7 states that if subtracting twice the last digit of the given number from the remaining digits gives a multiple of 7, then the given number is divisible by 7.
1.  What is Divisibility? 
2.  Definition of Divisibility 
3.  
4.  Divisibility Rule of 7 
5.  Solved Examples 
6.  Practice Questions 
7.  FAQs on Divisibility 
What is Divisibility?
Divisibility means to check if a number is divisible by another number without actually dividing the number. There are a set of conditions to know if a number is perfectly divisible by another number. A number may or may not be perfectly divisibe by another number, but knowing the divisibility rules makes calculation faster and easier.
Definition of Divisibility
A number is said to be divisible, if the divisor completely divides the number without leaving a remainder. For example, to check if 10 is divisible by 2, we see that when 10 is divided by 2, it does not leave any remainder, other than 0. This means 10 passes the divisibility test of 2.
Most Commonly Used Divisibility Rules
Let us precisely have an overview of the most commonly used divisibility rules.
 Divisibility by 2
If a number is an even number, or the last digit of the number is 2, 4, 6, 8 and 0, then it is divisible by 2.  Divisibility by 3
If the sum of all the digits in the number is divisible by 3, then the number is divisible by 3.  Divisibility by 4
If the last two digits of the number are divisible by 4, then the number is divisible by 4.  Divisibility by 5
If a number has 0 or 5 as the last digit, then it is divisible by 5.  Divisibility by 6
If a number is divisible by both 2 and 3, then it is divisible by 6.  Divisibility by 8
If the last three digits of a number are divisible by 8, then the number is divisible by 8.  Divisibility by 9
If the sum of the digits of the number are divisible by 9, then it the number is divisible by 9.  Divisibility by 10
A number which has the last digit as 0, is divisible by 10.
Divisibility Rule of 7
Let us now learn how to check if a number is divisible by 7. As we have already discussed, a number is perfectly divisible by another number if it does not leave any remainder and the quotient is a whole number. The same rule applies to the divisibility by 7. Observe the following figure to learn the divisibility rules for 7.
Let us apply these rules on a given number. Observe the following figure to check if 2455 is divisible by 7.
Topics Related to Divisibility
Important Topics
Solved Examples

Example 1: Is 2415 divisible by 7?
Solution:
Step 1: Multiply the last digit (5) by 2. The product is 10,
Step 2: Subtract the product (10) from the rest of the number, which is 241. (241  10 = 231)
Step 3: We do not know if 231 is a multiplie of 7. So, let us go back to step 1.
Step 4: Multiply the last digit (1) by 2. The product is 2.
Step 5: Subtract it from the rest of the number, which is 23. (23  2 = 21)
Step 6: Is 21 divisible by 7? Yes, so we can conclude that 2415 is divisible by 7. 
Example 2: Robin wants to know if 3216 is divisible by 7. Can you help him?
Solution:
Step 1: Multiply the last digit (6) by 2. The product is 12.
Step 2: Subtract the product (12) from the rest of the number, which is 321. (321  12 = 309)
Step 3: We do not know if 309 is a multiplie of 7. So, let us go back to step 1.
Step 4: Multiply the last digit (9) by 2. The product is 18.
Step 5: Subtract it from the rest of the number, which is 30. (30  18 = 12)
Step 6: Is 12 divisible by 7? No, so we can conclude that 3216 is NOT divisible by 7.
FAQs on Divisibility Rules
What is Divisibility?
Divisibility is a rule to check if a number is completely divisible by another number. In other words, a number is said to be divisible by another number if the remainder is zero and the quotient is a whole number.
Does Division and Divisibility Mean the Same?
No, division and divisibility are two different terms. Division is an arithmetic operation which divides a certain number of objects or a number into equal groups, whereas, the divisibility test checks if a number is perfectly divisible by a divisor without actually dividing the number by the division method.
Do Divisibility Rules Apply Only for Prime Numbers?
No, divisibility rules apply for non prime numbers as well.
What is the Formula for Divisibility?
There are different rules and formulas for checking the divisibility of numbers. For example, to check the divisibility of a number by 2, we need to check if the last digit is an even number. The rule for the divisibility of 3 states that if the sum of all the digits of the given number is divisible by 3, then the number is divisible by 3.
Are all Numbers Divisible by 1?
Yes, all numbers are divisible by 1.
When Can we Say that a Number is not Divisible by Another Number?
When a dividend is divided by a divisor, leaving a non zero remainder we can say that the number is not perfectly divisible by another number.