Consider the prime factorization of 1000:
[tex]1000=10\cdot 10\cdot10=(2\cdot5)\cdot(2\cdot5)\cdot(2\cdot5)=2^3\cdot5^3 [/tex]
We see that the prime factorization of 1000 contains 5 repeating three times and 2 repeating three times.
We can keep 5 repeating 3 times,
We can write a prime whose square is larger than [tex]2^3[/tex], for example: [tex]7^2[/tex]
Then we can write any prime which does not repeat, for example 2.
Thus the number we formed is [tex]2 \cdot7^2\cdot5^3=12,250[/tex]
Answer: 12,250
