Question

Find out the largest 5 digit number from the following numbers which is divisible by 14.
A.99989
B.99988
C.99888
D.10000

Answer 1

Hint: We know that number is divisible by 14 if it is divisible by 2 and 7. So take the largest number from the given numbers and check if it is divisible by 2 and 7 or not. If it is divisible then that will be our answer, otherwise go for the second largest number and check.

Complete step-by-step answer:

A number is divisible by 14 means if we divide a given number by 14 then the remainder should be zero. As we know that the factors of 14 are 2 and 7, we can say that a number is divisible by 14 if it is divisible by 2 and 7.
Now, we can easily check the divisibility for 2. If the given number is even then it will be divisible by 2.
From our options we can see that option (a) is an odd number. Therefore, it is not divisible by 2 and hence, it is not divisible by 14.
But the other three options are even numbers. Therefore, they are divisible by 2.
Now, we have to check the divisibility for 7.
Since we need to find out the largest number, let us start with option (b), which is the largest number.
Here is a rule which can be utilized to test divisibility by 7.
Remove the last digit of the given number, double it, subtract it from the truncated original number and continue doing it until one digit remains. If this is 0 or 7, then the given number is divisible by 7.
So the given number is 99988. The last digit of this number is 8. Double of 8 is 16. 9998 – 16 = 9982
Now the last digit is 2. Double of 2 is 4. 998 – 4 = 994.
The last digit is 4. Double of 4 is 8. 99 – 8 = 91.
Last digit is 1. Double of 1 is 2. 9 – 2 = 7.
Thus, 99988 is divisible by 7.
Since, 99988 is divisible by 2 and 7 both, it is divisible by 14.
And 99988 is the largest number here.
Hence, option (b) is correct.

Note: Divisibility by 14 can be checked also by using long division, but this process can be quite time consuming. Especially when faced with a very large number.