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Numbers under 100 with three different prime factors are 30, 42, 66, 70 and 78.

Numbers under 100 with three different prime factors, at least one of which has multiplicity > 1 are 8, 12, 18, 20, 27, 28, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98 and 99.

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10y ago
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10y ago

They are:

8, 12, 18, 20, 27,

28, 30, 42, 44, 45,

50, 52, 63, 66, 68,

70, 75, 76, 78, 92,

98, 99.

There are some that have more than 3 - which means that they do have 3.

[That last part is like the old riddle: how many months have 28 days - and the answer is all of them. Eleven have more than 28, but they do have 28.]

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Q: What numbers under 100.prime have 3 prime factors?
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There are no prime numbers anywhere that are divisible by 2 and 7.


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Numbers under 100 that have 12 factors must be in the form of ( p_1^{11} ) or ( p_1^3 \times p_2^2 ), where ( p_1 ) and ( p_2 ) are distinct prime numbers. The prime factorization of 12 is ( 2^2 \times 3 ). Thus, the numbers under 100 with exactly 12 factors are ( 2^{11} = 2048 ) and ( 2^3 \times 3 = 24 ).


What is the prime factorization of numbers 1 to 200?

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