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| A Digital Root Problem (Posted on 2006-06-29) |
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The digital root of a number is obtained by summing its digits and then repeating the process (summing the sum's digits) until the answer is a single digit number. For example, the digital root of 7368 is 6.
Determine the digital root of (97240+38)8457
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Submitted by K Sengupta
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Rating: 4.0000 (2 votes)
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Solution:
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(Hide)
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The required digital root is 8.
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METHOD 1 (Submitted by Daniel):
The solution submitted by Daniel is given here which follows the hint.
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METHOD 2:
Digital Root of :
(97240 + 38)8457
= Digital Root of :
(28457 + 9* A Large Number)
= Digital Root of :
(82819) + 9
= Digital Root of :
((9-1)2819 + 9)
= Digital Root of :
( (9*(A large number) - 1) + 9)
= Digital Root of :
(9 - 1+ 9)
= 8
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METHOD 3:
97240 + 38
= 38 (Mod 9)
= 2 (Mod 9)
Accordingly:
(97240 + 38)8457
= 28457 (Mod 9)
= 82819(Mod 9)
=(-1)2819 (Mod 9)
= (-1) (Mod 9)
= 8 ( Mod 9)
Since, the remainder of the given number (97240 + 38)8457 upon division by 9 is 8, and 8 is not congruent to 0 Mod 9, it follows from Raman's Formula that the required digital root must be 8.
NOTE : Definitions of Mod n are given in this location as well as here .
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