DIGITAL SUM of the numberGiven a number \(N_z\) , all the digits of N are added to obtain a number \(N_y\). All the digits of N are added to obtain a number \(N_x\), and so on, till we obtain a single digit number \(N\). This single digit number \(N\) is called the digital sum of the original number \(N_z\).
What is the digital sum of 84001 ?
Answer: 8+4+0+0+1 = 13 = 1+3 = 4 Hence, the digit sum of the number is 4.
Note: In finding the digital sum of a number we can ignore the digit 9 or the digits that add up to 9.
For example, in finding the digital sum of the number 246819, we can ignore the digits 2, 6, 1, and 9. Hence,
the digital sum of 246819 is = 4 + 8 = 12 = 1 + 2 = 3.
Digital Sum Rule of Multiplication: The digital sum of the product of two numbers is equal to the digital sum of the product of the digital sums of the two numbers.
Example: The product of 129 and 35 is 4515.
Digital sum of 129 = 3 and digital sum 35 = 8. Product of the digital sums = 3 × 8 = 24 Digital sum = 6.
Digital sum of 4515 is = 4 + 5 + 1 + 5 = 15 = 1 + 5 = 6. Digital sum of the product of the digital sums =
digital sum of 24 = 6 Digital sum of the product (4515) = Digital sum of the product of the digital sums
(24) = 6
Applications of Digital Sum :
1.Rapid checking of calculations while multiplying numbers :Suppose a student is trying to find the product 316 × 234 × 356, and he obtains the number 26525064. A
quick check will show that the digital sum of the product is 3. The digital sums of the individual numbers
(316, 234 and 356) are 1, 9, and 5. The digital sum of the product of the digital sum is 1 × 9 × 5 = 45 = 4 + 5 = 9. ⇒ the digital sum of the product of the digital sums (9) ≠ digital sum of the 26525064 (3). Hence,
the answer obtained by multiplication is not correct.
Note: Although the answer of multiplication will not be correct if the digital sum of the product of the digital
sums is not equal to digital sum of the product, but the reverse is not true i.e. the answer of multiplication
may or may not be correct if the digital sum of the product of the digital sums is equal to digital sum of
the product.
Suppose you have a question : ( Very absurd eg by me but learn the concept )
What is value is A+B+C+D+E?
\(878373 * 7738838339 * 827287 = E6D35C50B5547A87623729\)
HINT: Find the digital sum on LHS and equate it with that of RHS.
2.Determining if a number is a perfect square or not :The digital sum of the numbers which are perfect squares will
always be 1, 4, 7, or 9.
Note: A number will NOT be a perfect square if its digital sum is NOT 1, 4, 7, or 9, but it may or may not
be a perfect square if its digital sum is 1, 4, 7, or 9.
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