Under 50

Number Theory Level 3

How many positive integer under 50 have exactly 2 distinct primes factors? No repeats, $(2^{2})$ $(3^{2})$ doesn't count.

The answer is 13.

1 solution

Arulx Z
Jan 20, 2016

Only possible way to have 2 factors is to have a number of form $pq$ , where both $p$ and $q$ are primes (raised to the power of 1). Since $29 \cdot 2 > 50$ , the primes are less than or equal to 23.

So we need to calculate the combinations of product of primes with product less than 50.

2 can be multiplied with 3, 5, 7, 11, 13, 17, 19, 23

3 can be multiplied with 5, 7, 11, 13

5 can be multiplied with 7

For all other, we either need to repeat a pair or the product is greater than 50. Therefore the answer is 13.

Under 50

The answer is 13.

1 solution

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