Question
1)) Type a digit that makes this statement true 307,583 is divisible by 3 .
Ask by Mullins Fernandez. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
A digit that makes **307,583** divisible by **3** is **1**.
Solution
To determine a digit that makes the number **307,583** divisible by **3**, follow these steps:
### **Divisibility Rule for 3**
A number is divisible by **3** if the **sum of its digits** is divisible by **3**.
### **Step 1: Calculate the Sum of the Digits**
Let's add the digits of **307,583**:
\[
3 + 0 + 7 + 5 + 8 + 3 = 26
\]
### **Step 2: Determine the Required Digit**
Since **26** is not divisible by **3**, we need to find a digit **\(x\)** such that:
\[
26 + x \equiv 0 \ (\text{mod} \ 3)
\]
This means:
\[
x \equiv 1 \ (\text{mod} \ 3)
\]
Possible digits for **\(x\)** that satisfy this condition are **1, 4,** and **7**.
### **Conclusion**
Any of the digits **1, 4,** or **7** appended to **307,583** will make the number divisible by **3**.
**For example:**
- **307,5831**
- **307,5834**
- **307,5837**
All of these numbers are divisible by **3**.
**So, a valid digit to make the statement true is:**
**1**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To check if a number is divisible by 3, you can sum its digits and see if that sum is divisible by 3. For 307,583, the sum of the digits is 3 + 0 + 7 + 5 + 8 + 3 = 26. Since 26 isn't divisible by 3, we need to find a digit to add to reach the next multiple of 3. Adding 2 would make the total 28, which is not enough, but adding 4 makes it 30, which is divisible by 3. Therefore, the digit you need to add is 4! Adding 4 brings the sum of the digits to 30, confirming that 307,583 becomes divisible by 3. Now you can impress your friends with your math skills, and always remember to check the digits when divisibility questions pop up!
