Question

A number greater than 1000 whose prime factorization contains one prime number that does not repeat one prime number that repeats three times and one prime number that repeats twice

Answer 1

It wont let me see the answer usless i add one myself so ignore this

Explanation:

Answer 2

Consider the prime factorization of 1000:


`1000=10\cdot 10\cdot10=(2\cdot5)\cdot(2\cdot5)\cdot(2\cdot5)=2^3\cdot5^3`

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
`2^3`, for example:
`7^2`

Then we can write any prime which does not repeat, for example 2.


Thus the number we formed is
`2 \cdot7^2\cdot5^3=12,250`


Answer: 12,250