What 2 prime numbers times together makes 165?

Answer 1

Prime factorization is a very difficult problem, and top mathematicians and computers have not solved it. But for small numbers, it is possible to use trial and error to find the prime factorization of the number. The first thing to note is that if a number is the product of two prime numbers, neither prime is larger than the square root of the number. So, for 165, √165 ~ 13. So, now comes the trial and error. Is it divisible by 2? No, it's not an even number. Is it divisible by 3? Let's see, do the individual numbers add up to a multiple of 3? 1+6+5=12 and 1+2=3. So, 3 is one factor. Now that we know the first factor, it's just a simple division problem to find the other factor. 165/3 = 55.

But wait a minute; 55 isn't prime. It's 5*11. So the prime factors of 165 are 3, 5 and 11. This means that there are no "2" prime numbers that multiply to 165. There are 3 prime numbers that multiply to 165.