About Divisibility Rule of 7
The Divisibility Rule
The divisibility rule, also known as the divisibility test, is a technique used in mathematics to determine, without executing the complete division operation, if a given integer is divisible by a divisor.
The technique could be as simple as checking if the number is odd or even, as in the case of the number ‘2’ or in the case of ‘3’, it is adding the digits of the number and checking if the sum is divisible by three and so on.
There are different divisibility rules for different numbers. The ‘Divisibility Rule of Seven’ will be covered in this article along with numerous applications of the same concept.
Divisibility Rule of 7
When a number is divided by 7 and the remainder is 0, then we can say that the given number is divisible by 7.
For example, 77 \(\div\) 7 = 11 R0.
Hence, 77 is divisible by 7 as the remainder is 0 when this division operation is done.
There is another fun way to check if a number is divisible by 7 or not.
If a number is divisible by seven, then ‘the difference between twice the ones digit of the provided number and the remaining part of the given number should be a multiple of seven or it should be equal to zero’.
For example, let’s check if 224 is divisible by 7 or not.
The ones digit in 224, is 4. When the ones digit is doubled, the result is 4 x 2 = 8.
22 is the remaining part of the number under consideration.
Now, subtract 8 from 22 to get the difference.
22 – 8 = 14
The difference between the two numbers, in this case, is 14, a multiple of 7 (since, 7 x 2 = 14).
Therefore, the number 224 is divisible by 7.
Solved Examples
Example 1:
Check if the following numbers are divisible by 7.
a. 693
b. 118
Solution:
(a) 693
\(\frac{693}{7}\) = 99 R0. When 693 is divided by 7, the remainder is 0. Hence, 693 is divisible by 7.
(b) 118
\(\frac{118}{7}\) = 16 R6. When 118 is divided by 7, the remainder is 6. Hence, 118 is not divisible by 7.
Example 2:
Check whether the number 449 is divisible by 7.
Solution:
The number provided = 449.
To check whether 449 is divisible by 7:
Step 1: Double the ones 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.
Example 3:
There are six seats in each pod of a small ferris wheel. There are seven such pods throughout the wheel. Can 50 students be distributed equally across the pods? If the 50 students are randomly seated on the wheel, would there be any vacant places on the wheel?
Solution:
Number of seats in each pod = 6
Number of pods = 7
Number of students = 50
All the students have to be equally distributed into the pods. Hence, we need to check if 50 is divisible by 7.
\(\frac{50}{7}\) = 7 R1. When 50 is divided by 7, the remainder is 1. Hence 50 is not divisible by 7.
So, 50 students cannot be equally distributed into 7 pods.
To check if there are any vacant spaces on the wheel after the 50 students are seated, we need to first find the total number of seats on the wheel.
Number of seats on the wheel = 7 x 6 = 42
50 > 42, that is, the number of students is greater than the number of seats available.
Therefore, there are no vacant seats on the ferris wheel.
When a number is divided by 7 and the remainder is 0, then the number is divisible by 7. Without executing the division operation, another way to check if a number is divisible by 7 is, if the difference between twice the unit digit of the given number and the remaining portion of the provided number is equal to 0 or a multiple of 7.
There are 14 numbers between 1 and 100 that can be divided by 7 precisely.
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 and 98 are the numbers.
When the given number is divided by 7 and the remainder is 0, then the number is a multiple of 7. In other words, if a number is divisible by 7, then it is a multiple of 7.