Question
Without dividing, determine if 45,678 is divisible by 3 and explain how you know. Answer Attempt 2 out of 2 \( 45,678 \quad \) divisible by 3 Submit Answer
Ask by Norton Fleming. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 45,678 \) is divisible by 3 because the sum of its digits (\( 4 + 5 + 6 + 7 + 8 = 30 \)) is divisible by 3.
Solution
To determine if a number is divisible by 3, we can use the rule of divisibility for 3, which states that a number is divisible by 3 if the sum of its digits is divisible by 3.
Let's apply this rule to the number \( 45,678 \):
1. **Extract the digits**: The digits of \( 45,678 \) are \( 4, 5, 6, 7, \) and \( 8 \).
2. **Calculate the sum of the digits**:
\[
4 + 5 + 6 + 7 + 8
\]
3. **Perform the addition step by step**:
- First, add \( 4 + 5 = 9 \).
- Next, add \( 9 + 6 = 15 \).
- Then, add \( 15 + 7 = 22 \).
- Finally, add \( 22 + 8 = 30 \).
4. **Sum of the digits**: The total sum is \( 30 \).
5. **Check if the sum is divisible by 3**: Now, we need to check if \( 30 \) is divisible by \( 3 \):
- Calculate \( 30 \div 3 = 10 \), which is a whole number.
Since \( 30 \) is divisible by \( 3 \), we conclude that the original number \( 45,678 \) is also divisible by \( 3 \).
Thus, \( 45,678 \) is divisible by \( 3 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To determine if 45,678 is divisible by 3, you can use a simple rule: just add the digits together! In this case, let's add 4 + 5 + 6 + 7 + 8, which equals 30. Since 30 is divisible by 3 (as 30 ÷ 3 = 10), it follows that 45,678 is also divisible by 3. This trick works because 3 is a factor of any number formed by its digits. So, if the sum of the digits can be divided by 3 without leaving a remainder, then the original number will also be divisible by 3. It’s a neat shortcut that keeps you from pulling out a calculator!
