0 mod 8
Understand the Problem
The question is asking for the remainder when 0 is divided by 8. This is a straightforward calculation in modular arithmetic.
Answer
The remainder is $0$.
Answer for screen readers
The remainder when 0 is divided by 8 is $0$.
Steps to Solve
- Understanding Remainder Definition
To find the remainder when dividing two numbers, we can express the division in the form of an equation: $$ a = bq + r $$ where:
- ( a ) is the dividend (in this case 0),
- ( b ) is the divisor (in this case 8),
- ( q ) is the quotient (the result of the division),
- ( r ) is the remainder.
- Substituting Values into the Equation
For our problem, substitute ( a = 0 ) and ( b = 8 ) into the equation: $$ 0 = 8q + r $$
- Finding the Remainder
Since ( 8q ) represents the largest multiple of 8 that is less than or equal to 0 and ( r ) is what remains, the only value that satisfies this equation is when ( r = 0 ). This is because ( 8q ) can only be 0 when ( q ) is also 0.
- Conclusion
Therefore, the remainder when 0 is divided by 8 is: $$ r = 0 $$
The remainder when 0 is divided by 8 is $0$.
More Information
In mathematics, dividing zero by any non-zero number always results in a quotient of zero with a remainder of zero. This reflects the fundamental property of division and modular arithmetic.
Tips
- Forgetting that dividing zero by any non-zero number always results in a remainder of zero. To avoid this mistake, always remember that the division by zero scenario is different and should be noted.
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