The greatest 4-digit number is 9999.
To express 9999 in terms of its prime factors, we first need to perform a factorization. We can start by dividing 9999 by the smallest prime number, which is 3:
9999 ÷ 3 = 3333
Now, we can factor 3333 further:
3333 ÷ 3 = 1111
Next, we factor 1111. The next smallest prime is 11:
1111 ÷ 11 = 101
Finally, we see that 101 is a prime number and cannot be factored further.
Putting it all together, the prime factorization of 9999 is:
9999 = 3^2 × 11 × 101
This means that 9999 can be expressed as the product of 3 multiplied by itself twice, multiplied by 11 and then by 101.