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Rama09 [41]
3 years ago
10

A number greater than 1000 whose prime factorization contains one prime number that does not repeat one prime number that repeat

s three times and one prime number that repeats twice
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
6 0
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
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