1. **Stating the problem:** We have a list of numbers with decimals and want to decompose each into whole numbers by dividing by a divisor with 3 to 4 digits (i.e., between 100 and 9999). 2. **Understanding the problem:** Decomposition here means expressing each number as $\text{number} = \text{divisor} \times \text{quotient}$ where divisor is a 3- or 4-digit whole number and quotient is a whole number. 3. **Step to find the divisor:** We want a common divisor for all numbers that is a 3- or 4-digit integer and divides each number exactly (no decimals after division). 4. **Convert all numbers to integers:** Since decimals are .00 or .13 or .61 etc., multiply each number by 100 to remove decimals and work with integers: Example: $642352.00 \to 64235200$, $2963856.47 \to 296385647$, etc. 5. **Find the greatest common divisor (GCD) of all these integers:** The GCD will be the largest integer dividing all numbers exactly. 6. **Check if the GCD is a 3- or 4-digit number:** If not, find a divisor of the GCD that fits the 3-4 digit requirement. 7. **Calculate GCD:** Using the numbers multiplied by 100: $64235200, 296385647, 204958000, 271788000, 335305520, 332370000, 335880000, 331059116, 192928313, 825000000, 337509361, 51610500, 308069328, 955200000, 232440800, 336070000, 1540672269, 255042017, 144846387, 325456297, 523397400, 276218607, 350388041, 221000000, 378300000, 1732651824, 1687000000, 701800000$ 8. **Approximate GCD:** Since many numbers end with zeros, the GCD will be at least 100 (due to multiplying by 100). Checking divisibility by 100 is trivial. 9. **Check common factors:** The numbers vary widely, but many end with zeros, so 100 is a common factor. 10. **Try to find a larger divisor:** For example, 1000 or 10000 may not divide all numbers exactly. 11. **Conclusion:** The common divisor with 3-4 digits that divides all numbers exactly is 100. 12. **Decompose each number by dividing by 100:** Example: $642352.00 \div 100 = 6423.52$ (not whole), so 100 is not exact divisor for all. 13. **Try to find a divisor that divides all numbers exactly without decimals:** Since some numbers have decimals like .47, .13, .61, exact division by 100 or 1000 is not possible. 14. **Alternative approach:** Since decimals are up to 2 decimal places, multiply all numbers by 100 to get integers, then find GCD of these integers. 15. **Calculate GCD of all integers (multiplied by 100):** The GCD is 1 (since some numbers have decimals like .47, .13, .61 which are not multiples of 1/100). 16. **Therefore, no common divisor greater than 1 divides all numbers exactly after scaling. 17. **Find common number between these numbers:** The problem likely asks for the greatest common divisor (GCD) or a common factor. 18. **Since GCD is 1, the only common number is 1.** **Final answer:** - No 3- or 4-digit divisor divides all numbers exactly without decimals. - The only common number dividing all is 1. - Decomposition into whole numbers with such divisor is not possible for all numbers. **Summary:** $$\text{Common divisor} = 1$$ $$\text{No 3- or 4-digit divisor divides all numbers exactly}$$