Factors

[shreyas.rf]

If p is a positive integer less than 75 and 3p/84 is an integer,
then p has how many di§erent positive prime factors?

[Jazmet]

Since 3p/84 is an integer, it states that 3p is divisible by all the prime factors of 84. (for example - 8/4 - 8 has all the prime factors of 4 and including their powers) - hence we need to break down 84 - 2 x 2 x 3 x 7.

Since 3 is already mentioned in the numerator, 'P' is bound to have all the remaining primes with their powers. So, 'P' has two more prime factors i.e. 2 and 7.

Hence the answer is two.

[jnelson0612]

Excellent work, Jazmet!

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