Divisibility Test of 14

What is the Divisibility of a Number?

A number is said to be totally divisible by any number if it yields a quotient as a whole number and the remainder is zero. 

For example, 24 is said to be divisible by 6 as 24/6 yields 4 as a quotient which is a whole number. But 24/5 = 4.8 which is not a whole number. Hence, 24 is not divisible by 5.

Every number is divisible by 1 as the number divided by 1 yield the number as a quotient.

Need of Divisibility Tests

Divisibility is often considered important as it sometimes becomes necessary to know whether a number divides another number. This process is easy for smaller numbers, but it becomes difficult and tedious for larger numbers. 

Therefore, divisibility tests are made so that we do not have to actually divide a number to check whether it is divisible or not. It is very useful as it saves our time and labor. 

Divisibility Test of 14

Rule 1: A number that is completely divisible by 2 and 7 is said to be divisible by 14. Therefore, if a number is to be checked that it is divisible by 14, then the tests mentioned above should be followed.

Rule 2: Add the last two digits of the number with twice the rest of the digits. If the result sum is divisible by 14, then the number is said to be divisible by 14. 

Divisibility Test of 14 with Examples

Example 1. Check whether 1764 is divisible by 14.

Solution: 

• Firstly, check whether the number is divisible by 2 and 7. 

• 1764 is divisible by 2 and 7. Thus, the divisibility test of 14 is satisfied.

• Hence, 1764 is divisible by 14.

Example 2. Check whether 784 is divisible by 14.

Solution:

• Add the last two digits of the number to twice the rest of the digits.

• 84 + (2 X 7) = 98

• 98 is completely divisible by 14.

• Hence, 784 is divisible by 14.

Example 3. Check whether 1245 is divisible by 14.

Solution:

• Add the last two digits of 1245 to twice the rest of the digits.

• 45 + (12 X 2) = 69

• 69 is not divisible by 14.

• Hence, we can say that 1245 is not divisible by 14. 

Example 4. Check whether 896 is divisible by 14.

Solution:

• Add the last two digits of 896 to twice the rest of the digits.

• 96 + (8 X 2) = 112

• 112 is divisible by 14.

Hence, we can say that 896 is completely divisible by 14.

Conclusion

Through this guide, we got to learn about the divisibility test of 14 with examples. Otherwise, it would have been a very difficult task to check whether a number is divisible by 14 if the number is large.

Now, by going through this article we got to learn about the rules which we would apply in order to check the divisibility test of 14.

 We just have to find out whether the number is divisible by 2 and 7. Or the second method is to add the last two digits of the number to twice the rest of the number. If the resultant sum is divisible by 14 then we can say that the number is completely divisible by 14.

By using the tests, our workload is reduced by a greater amount.