Number System: Get DIGITAL with DIGITAL ROOT

Special for IBPS EXAMS Number System: Get DIGITAL with DIGITAL ROOT One of the short cut which you must learn in Number System is that of Digital Roots. This amazing concept of Digital Roots will help you solve numerous questions on remainders, divisibility and sum of digits. Keep in mind that from now onwards in the article, the term ‘digital root’ will be referred to as DR. DR (also known as repeated digital sum/seed number) of a number is the number obtained by adding all the digits, then adding the digits of that number, and then continuing until a single-digit number is obtained. First try to understand this with the help of the following examples: Example: DR (48512) = DR (4+8+5+1+2) = DR (20) = DR (2+0) = 2. Example: DR (9873429222) = DR (9+8+7+3+4+2+9+2+2+2) = DR (48) = DR (4+8) = DR (12) = DR (1+2) = 3. Divisibility Rule of 9:  What is the remainder when 48512 is divided by 9? In order to check for the divisibility of a number by 9, we add all the digits and check the remainder of these with 9. Here the approach we follow is that we determine the sum of digits (SOD) = 4+8+5+1+2 = 20=2+0=2. So, the remainder when the number 48512 is divided by 9 is 2. Example 1:  What is remainder when 9873429222 is divided by 9? Solution: Again the divisibility rule of 9 will be applied. 9+ 8 + 7 + 3 + 4 + 2 + 9 + 2 + 2 + 2 = 48 = 4 + 8 = 12 = 1+ 2 =3 So, remainder is 3 in this case. It can be concluded from the above examples that whether we take DR of any number say N or remainder when N is divided by 9, the answers are same. Actually both these concepts are same. To review the same, it can be stated that if a number has a DR 1, it will leave a remainder 1 when divided by 9. If it has a DR 2, the remainder will be 2 and so on, till the last point where if it has a DR 9, the remainder will be 0, when divided by 9. Example 2: What is the digital root of 26! (factorial)? Solution: Since 26! has the product of all the digits from 1 till 26, it will be divisible by 9. Or in other words, it will have a digital root equal to 9. Example 3: How many natural number < 500 exist whose seed number is 9? Solution: Digital root or seed number means remainder is 0 when number is divided by 9. So, question is “How many natural numbers < 500 divisible by 9” and it can be calculated that there are 500/9 = 55 such numbers as it is starting from 1 only. Thus, 55 will be the answer. Best Wishes !!!!!!!!!!!!! Sahil