What is the remainder when 8127 is divided by 8?
7
Understanding the Remainder in Division
When we divide one whole number (the dividend) by another whole number (the divisor), we get a quotient and a remainder. The remainder is the amount left over that cannot be evenly divided by the divisor. It is always less than the divisor.
Finding the Remainder: 8127 Divided by 8
We need to find the remainder when the number 8127 is divided by 8. For larger numbers, especially when dividing by 8, there's a helpful divisibility rule that simplifies the process.
Divisibility Rule for 8
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. Consequently, the remainder when a large number is divided by 8 is the same as the remainder when the number formed by its last three digits is divided by 8.
In the number 8127, the last three digits form the number 127.
Step-by-Step Calculation of the Remainder
To find the remainder when 8127 is divided by 8, we will find the remainder when 127 is divided by 8.
We perform the division of 127 by 8:
$$ 127 \div 8 $$
We can find out how many times 8 fits into 127:
- $8 \times 10 = 80$
- Remaining amount: $127 - 80 = 47$
- Now, how many times does 8 fit into 47?
- $8 \times 5 = 40$
- Remaining amount: $47 - 40 = 7$
Since 7 is less than 8, it is our remainder.
So, we can write the division as:
$$ 127 = (8 \times 10) + (8 \times 5) + 7 $$
$$ 127 = 8 \times (10 + 5) + 7 $$
$$ 127 = 8 \times 15 + 7 $$
Here, the quotient is 15 and the remainder is 7.
According to the divisibility rule for 8, the remainder of 8127 divided by 8 is the same as the remainder of 127 divided by 8.
Therefore, the remainder when 8127 is divided by 8 is 7.
Revision Table: Key Division Concepts
| Term | Definition | Example (10 ÷ 3) |
|---|---|---|
| Dividend | The number being divided. | 10 |
| Divisor | The number by which another number is divided. | 3 |
| Quotient | The result of division, excluding the remainder. | 3 |
| Remainder | The amount left over after division. Always less than the divisor. | 1 ($10 = 3 \times 3 + 1$) |
Additional Information: More Divisibility Rules for Numbers
Divisibility rules are shortcuts to determine if a number is divisible by another number without performing the full division. Here are a few common ones:
- Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
- Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Divisibility by 10: A number is divisible by 10 if its last digit is 0.
Understanding these rules can help solve division and remainder problems more quickly.
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