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Chapter 2: Problem 31

Determine whether 1880 is divisible by 8

Short Answer

Expert verified
Yes, 1880 is divisible by 8.

Step by step solution

01

Understand the Divisibility Rule for 8

A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.
02

Extract the Last Three Digits

1880 has the last three digits '880'.
03

Check Divisibility of 880 by 8

Now, check if 880 is divisible by 8. Perform the division: \( 880 \, / \, 8 \). Calculate the result: \( 880 \, / \, 8 = 110 \). Since 880 divided by 8 equals 110 exactly and there is no remainder, 880 is divisible by 8.
04

Conclude Divisibility

Since the last three digits (880) are divisible by 8, the original number 1880 is also divisible by 8.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

divisibility by 8
To determine if a number is divisible by 8, you need to apply a simple but powerful rule. A number is divisible by 8 if its last three digits form a number that is divisible by 8. For example, let鈥檚 take the number 1880.
The last three digits of 1880 are '880'. Now, we focus only on '880' to check for divisibility by 8.
This leads us straight into a small calculation to confirm it, and we'll discuss more calculations in the next section.
arithmetic division
Arithmetic division is a fundamental concept in mathematics where you split a number into equal parts. To determine divisibility, you perform a simple division calculation. Let鈥檚 practice this with our previous example.
We take the last three digits, '880', and divide by 8. So, it looks like this: \[ 880 / 8 = 110 \] As you can see, 880 divided by 8 equals 110 without any remainder.
Because there is no remainder, we conclude that 880 is perfectly divisible by 8.
Therefore, this calculation helps us confirm the rule explained in the first section. Sometimes, understanding arithmetic division is about seeing how larger numbers can be broken down.
mathematical problem-solving
Problem-solving in mathematics involves breaking down a problem into smaller, more manageable parts. Let's revisit our original example, 1880, to see this in action.
Here are the steps, simplified for clarity:
  • Extract the last three digits: For 1880, this is '880'.
  • Apply arithmetic division: Divide 880 by 8, as we did above.
  • Check for no remainder: Since 880 divided by 8 equals 110 exactly, 880 is divisible by 8.
Using these steps, we conclude that the entire number 1880 is also divisible by 8.
This systematic approach can be applied to other divisibility problems and helps you become more confident in tackling various mathematical challenges.

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