Remainder Calculation for 987654321
To find the remainder when 987654321 is divided by 9, we can use the divisibility rule for 9.
Divisibility Rule for 9
The rule states that a number is divisible by 9 if the sum of its digits is divisible by 9. The remainder when a number is divided by 9 is the same as the remainder when the sum of its digits is divided by 9.
Applying the Rule
First, calculate the sum of the digits of the number 987654321:
Sum = $9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1$
Sum = $45$
Next, find the remainder when this sum (45) is divided by 9:
Remainder = $45 \pmod{9}$
Since $45 = 9 \times 5$, the remainder is 0.
Conclusion
Therefore, the remainder when 987654321 is divided by 9 is 0.
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