Find the remainder on division of n=6,523,178 .....?

Question

Find the remainder on division of n=6,523,178 by 9 and then the remainder on division of the cube of n by 9.

Answer 1

6,523,178 => 6+5+2+3+1+7+8 = 32 => 3+2 = 5

the first remainder is 5
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6,523,178² / 9 ???

you take the first remainder ... 5² = 25 => 25 - 2*9 = 7

the second remainder is 7

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6,523,178^3 / 9 ???

you take the first remainder ... 5^3 = 125 => 125 - 13*9 = 8

the third remainder is 8

Answer 2

Using a calculator the remainder of n is 5. Therefore the remainder of the cube of n would be the remainder of 5^3 or 125 divided by 9 or 8.

Answer 3

The digital root of your number is 5, which will be the remainder of the division. Your cubed will have a remainder of 8 when divided by 9.

Answer 4

6523178 has a remainder of 5

so it's of the form 9x +5
(9x +5)^3

You can expand this out , but you don't need to include the terms that are multiplied by 9x(because it will be divisible by 9)

The remainder of (9x +5)^3 is the same as the remainder of 5^3 (or 125)
which has a remainder of 8

Answer 5

n mod 9 =5
n^3 mod 9 = ?

n^1=5 mod 9
n^2=7 mod 9

n^3=5.7=8 mod 9


the answer is 8