To determine which number should be subtracted from 876905 so that it is divisible by 8, we follow these steps:

Step 1: Check the divisibility rule for 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Step 2: Identify the last three digits of 876905

The last three digits are 905.

Step 3: Determine the remainder when 905 is divided by 8

We divide 905 by 8 to find the remainder:

$905 \div 8 = 113 \text{ remainder } 1$

This means 905 leaves a remainder of 1 when divided by 8.

Step 4: Subtract the remainder from 876905

To make the number divisible by 8, we need to subtract this remainder (1) from the number:

$876905 - 1 = 876904$

Step 5: Verification

Finally, let's verify by checking if 876904 is divisible by 8:

• The last three digits of 876904 are 904.
• Now, divide 904 by 8:

$904 \div 8 = 113 \text{ remainder } 0$

Since the remainder is 0, 876904 is divisible by 8.

Thus, the number to subtract from 876905 to make it divisible by 8 is 1.

Would you like further details or have any questions?

Related Questions:

1. What number should be added to 876905 to make it divisible by 8?
2. How can we determine if a large number is divisible by 16?
3. How do divisibility rules differ for various prime numbers?
4. What if we need to make a number divisible by 12 instead of 8?
5. How can you use modular arithmetic to solve similar problems?
6. What is the remainder when 876905 is divided by 16?
7. Can you find a general rule for adjusting numbers to be divisible by any integer?
8. How does the concept of divisibility apply to solving algebraic equations?

Tip: When dealing with divisibility, focus on the rules for the specific divisor to simplify the process.