## Friday, May 30, 2014

### Finding Missing Digit - Divisibility Rule, 7

Category: Arithmetic

"Published in Newark, California, USA"

Find the missing digit so that it becomes divisible by 8 for

a. 78?45
b. 2468?

Solution:

a. Consider the given number

Since the last digit of a given number is not an even number, then the given number is not divisible by 8. The multiples of 8 are all even number. There's nothing that we can do in order to become divisible by 8 since the last digit of a given number is not an even number. You can assign any number to the missing digit but still, the given number will never become divisible by 8.

b. Consider the given number

A number is divisible by 8 if the last three digit is a multiple of 8. Since the missing digit is the last digit, then we can assign even number digits so that the last three digit will be divisible by 8. If the last digit is 0, then 68 becomes 680 and 680 is divisible by 8. If the last digit is 2, then 68 becomes 682 and 682 is not divisible by 8. If the last digit is 4, then 68 becomes 684 and 684 is not divisible by 8. If the last digit is 6, then 68 becomes 686 and 686 is not divisible by 8. If the last digit is 8, then 68 becomes 688 and 688 is divisible by 8. Therefore, the possible numbers are 24680 and 24688.