The smallest 5 digit number exactly divisible by 31 is 10011.
Here's how to find it:
- Identify the smallest 5-digit number: The smallest 5-digit number is 10000.
- Divide by 31: Divide 10000 by 31. The result is approximately 322.58.
- Find the next whole number: Round the result up to the next whole number, which is 323.
- Multiply: Multiply 323 by 31. This gives you 10013.
- Adjust for accuracy: Realized that 10013 is divisible by 31 (32331), but the previous calculation 32231 leads to 9982. Since 10000/31 is approx. 322.58, then multiply 322*31 = 9982. 10000-9982 = 18.
- Calculate the required adjustment: Subtract the remainder from 31: 31 - 18 = 13.
- Add to the smallest 5-digit number: Add this value to the smallest 5-digit number: 10000 + 13 = 10013
- Since 10013 is not the correct answer, let's adjust. It seems there was an arithmetic error in step 4. To rectify the calculation we can follow these steps to get to the proper solution.
- Take the original problem: 10000/31
- This gives you 322.58
- We know the answer must be 323 x 31, so this means that is one number more than 322 x 31.
- (322 x 31 = 9982) and (323 x 31 = 10013)
- Adjust for accuracy to see if this is the smallest number. What if we tried 322? (322 x 31 = 9982.) 322 is one smaller, so this would not lead us to a 5 digit number.
- If you did 321 x 31 = 9951. Not a 5 digit number, so now we know 323 x 31= 10013 is the correct answer.
Therefore, 10013 is the smallest 5-digit number that is exactly divisible by 31.
